Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Code”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Use, Assessment, and Improvement of the Loci-CHEM CFD Code for Simulation of Combustion in a Single Element GO2/GH2 Injector and Chamber

This document is a viewgraph presentation of a paper that documents a continuing effort at Marshall Space Flight Center (MSFC) to use, assess, and continually improve CFD codes to the point of material utility in the design of rocket engine combustion devices. This paper describes how the code is presently being used to simulate combustion in a single element combustion chamber with shear coaxial injectors using gaseous oxygen and gaseous hydrogen propellants. The ultimate purpose of the efforts documented is to assess and further improve the Loci-CHEM code and the implementation of it. Single element shear coaxial injectors were tested as part of the Staged Combustion Injector Technology (SCIT) program, where detailed chamber wall heat fluxes were measured. Data was taken over a range of chamber pressures for propellants injected at both ambient and elevated temperatures. Several test cases are simulated as part of the effort to demonstrate use of the Loci-CHEM CFD code and to enable us to make improvements in the code as needed. The simulations presented also include a grid independence study on hybrid grids. Several two-equation eddy viscosity low Reynolds number turbulence models are also evaluated as part of the study. All calculations are presented with a comparison to the experimental data. Weaknesses of the code relative to test data are discussed and continuing efforts to improve the code are presented.

Westra, Douglas G.↗
NASA NTRS2009

LDPC-PPM Coding Scheme for Optical Communication

In a proposed coding-and-modulation/demodulation-and-decoding scheme for a free-space optical communication system, an error-correcting code of the low-density parity-check (LDPC) type would be concatenated with a modulation code that consists of a mapping of bits to pulse-position-modulation (PPM) symbols. Hence, the scheme is denoted LDPC-PPM. This scheme could be considered a competitor of a related prior scheme in which an outer convolutional error-correcting code is concatenated with an interleaving operation, a bit-accumulation operation, and a PPM inner code. Both the prior and present schemes can be characterized as serially concatenated pulse-position modulation (SCPPM) coding schemes. Figure 1 represents a free-space optical communication system based on either the present LDPC-PPM scheme or the prior SCPPM scheme. At the transmitting terminal, the original data (u) are processed by an encoder into blocks of bits (a), and the encoded data are mapped to PPM of an optical signal (c). For the purpose of design and analysis, the optical channel in which the PPM signal propagates is modeled as a Poisson point process. At the receiving terminal, the arriving optical signal (y) is demodulated to obtain an estimate (a^) of the coded data, which is then processed by a decoder to obtain an estimate (u^) of the original data.

Barsoum, Maged↗
NASA NTRS2009

From Verified Models to Verifiable Code

Declarative specifications of digital systems often contain parts that can be automatically translated into executable code. Automated code generation may reduce or eliminate the kinds of errors typically introduced through manual code writing. For this approach to be effective, the generated code should be reasonably efficient and, more importantly, verifiable. This paper presents a prototype code generator for the Prototype Verification System (PVS) that translates a subset of PVS functional specifications into an intermediate language and subsequently to multiple target programming languages. Several case studies are presented to illustrate the tool's functionality. The generated code can be analyzed by software verification tools such as verification condition generators, static analyzers, and software model-checkers to increase the confidence that the generated code is correct.

Lensink, Leonard↗
NASA NTRS2010

Short-Block Protograph-Based LDPC Codes

Short-block low-density parity-check (LDPC) codes of a special type are intended to be especially well suited for potential applications that include transmission of command and control data, cellular telephony, data communications in wireless local area networks, and satellite data communications. [In general, LDPC codes belong to a class of error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels.] The codes of the present special type exhibit low error floors, low bit and frame error rates, and low latency (in comparison with related prior codes). These codes also achieve low maximum rate of undetected errors over all signal-to-noise ratios, without requiring the use of cyclic redundancy checks, which would significantly increase the overhead for short blocks. These codes have protograph representations; this is advantageous in that, for reasons that exceed the scope of this article, the applicability of protograph representations makes it possible to design highspeed iterative decoders that utilize belief- propagation algorithms.

Divsalar, Dariush↗
NASA NTRS2011

Soft-Decision-Data Reshuffle to Mitigate Pulsed Radio Frequency Interference Impact on Low-Density-Parity-Check Code Performance

This presentation briefly discusses a research effort on mitigation techniques of pulsed radio frequency interference (RFI) on a Low-Density-Parity-Check (LDPC) code. This problem is of considerable interest in the context of providing reliable communications to the space vehicle which might suffer severe degradation due to pulsed RFI sources such as large radars. The LDPC code is one of modern forward-error-correction (FEC) codes which have the decoding performance to approach the Shannon Limit. The LDPC code studied here is the AR4JA (2048, 1024) code recommended by the Consultative Committee for Space Data Systems (CCSDS) and it has been chosen for some spacecraft design. Even though this code is designed as a powerful FEC code in the additive white Gaussian noise channel, simulation data and test results show that the performance of this LDPC decoder is severely degraded when exposed to the pulsed RFI specified in the spacecraft s transponder specifications. An analysis work (through modeling and simulation) has been conducted to evaluate the impact of the pulsed RFI and a few implemental techniques have been investigated to mitigate the pulsed RFI impact by reshuffling the soft-decision-data available at the input of the LDPC decoder. The simulation results show that the LDPC decoding performance of codeword error rate (CWER) under pulsed RFI can be improved up to four orders of magnitude through a simple soft-decision-data reshuffle scheme. This study reveals that an error floor of LDPC decoding performance appears around CWER=1E-4 when the proposed technique is applied to mitigate the pulsed RFI impact. The mechanism causing this error floor remains unknown, further investigation is necessary.

Ni, Jianjun David↗
NASA NTRS2003

P-Code-Enhanced Encryption-Mode Processing of GPS Signals

A method of processing signals in a Global Positioning System (GPS) receiver has been invented to enable the receiver to recover some of the information that is otherwise lost when GPS signals are encrypted at the transmitters. The need for this method arises because, at the option of the military, precision GPS code (P-code) is sometimes encrypted by a secret binary code, denoted the A code. Authorized users can recover the full signal with knowledge of the A-code. However, even in the absence of knowledge of the A-code, one can track the encrypted signal by use of an estimate of the A-code. The present invention is a method of making and using such an estimate. In comparison with prior such methods, this method makes it possible to recover more of the lost information and obtain greater accuracy.

Young, Lawrence↗
NASA NTRS2011

The Continual Intercomparison of Radiation Codes: Results from Phase I

The computer codes that calculate the energy budget of solar and thermal radiation in Global Climate Models (GCMs), our most advanced tools for predicting climate change, have to be computationally efficient in order to not impose undue computational burden to climate simulations. By using approximations to gain execution speed, these codes sacrifice accuracy compared to more accurate, but also much slower, alternatives. International efforts to evaluate the approximate schemes have taken place in the past, but they have suffered from the drawback that the accurate standards were not validated themselves for performance. The manuscript summarizes the main results of the first phase of an effort called "Continual Intercomparison of Radiation Codes" (CIRC) where the cases chosen to evaluate the approximate models are based on observations and where we have ensured that the accurate models perform well when compared to solar and thermal radiation measurements. The effort is endorsed by international organizations such as the GEWEX Radiation Panel and the International Radiation Commission and has a dedicated website (i.e., http://circ.gsfc.nasa.gov) where interested scientists can freely download data and obtain more information about the effort's modus operandi and objectives. In a paper published in the March 2010 issue of the Bulletin of the American Meteorological Society only a brief overview of CIRC was provided with some sample results. In this paper the analysis of submissions of 11 solar and 13 thermal infrared codes relative to accurate reference calculations obtained by so-called "line-by-line" radiation codes is much more detailed. We demonstrate that, while performance of the approximate codes continues to improve, significant issues still remain to be addressed for satisfactory performance within GCMs. We hope that by identifying and quantifying shortcomings, the paper will help establish performance standards to objectively assess radiation code quality, and will guide the development of future phases of CIRC

Oreopoulos, Lazaros↗
NASA NTRS2009

Proceedings of the Third International Workshop on Proof-Carrying Code and Software Certification

This NASA conference publication contains the proceedings of the Third International Workshop on Proof-Carrying Code and Software Certification, held as part of LICS in Los Angeles, CA, USA, on August 15, 2009. Software certification demonstrates the reliability, safety, or security of software systems in such a way that it can be checked by an independent authority with minimal trust in the techniques and tools used in the certification process itself. It can build on existing validation and verification (V&V) techniques but introduces the notion of explicit software certificates, Vvilich contain all the information necessary for an independent assessment of the demonstrated properties. One such example is proof-carrying code (PCC) which is an important and distinctive approach to enhancing trust in programs. It provides a practical framework for independent assurance of program behavior; especially where source code is not available, or the code author and user are unknown to each other. The workshop wiII address theoretical foundations of logic-based software certification as well as practical examples and work on alternative application domains. Here "certificate" is construed broadly, to include not just mathematical derivations and proofs but also safety and assurance cases, or any fonnal evidence that supports the semantic analysis of programs: that is, evidence about an intrinsic property of code and its behaviour that can be independently checked by any user, intermediary, or third party. These guarantees mean that software certificates raise trust in the code itself, distinct from and complementary to any existing trust in the creator of the code, the process used to produce it, or its distributor. In addition to the contributed talks, the workshop featured two invited talks, by Kelly Hayhurst and Andrew Appel. The PCC 2009 website can be found at http://ti.arc.nasa.gov /event/pcc 091.

Ewen, Denney, W.↗
NASA NTRS2016

Systematic Comparison of Photoionized Plasma Codes with Application to Spectroscopic Studies of AGN in X-Rays

Atomic data and plasma models play a crucial role in the diagnosis and interpretation of astrophysical spectra, thus influencing our understanding of the Universe. In this investigation we present a systematic comparison of the leading photoionization codes to determine how much their intrinsic differences impact X-ray spectroscopic studies of hot plasmas in photoionization equilibrium. We carry out our computations using the Cloudy, SPEX, and XSTAR photoionization codes, and compare their derived thermal and ionization states for various ionizing spectral energy distributions. We examine the resulting absorption-line spectra from these codes for the case of ionized outflows in active galactic nuclei. By comparing the ionic abundances as a function of ionization parameter, we find that on average there is about 30 deviation between the codes in where ionic abundances peak. For H-like to B-like sequence ions alone, this deviation in is smaller at about 10 on average. The comparison of the absorption-line spectra in the X-ray band shows that there is on average about 30 deviation between the codes in the optical depth of the lines produced at log 1 to 2, reducing to about 20 deviation at log 3. We also simulate spectra of the ionized outflows with the current and upcoming high-resolution X-ray spectrometers, on board XMM-Newton, Chandra, Hitomi, and Athena. From these simulations we obtain the deviation on the best-fit model parameters, arising from the use of different photoionization codes, which is about 10 to40. We compare the modeling uncertainties with the observational uncertainties from the simulations. The results highlight the importance of continuous development and enhancement of photoionization codes for the upcoming era of X-ray astronomy with Athena.

plasmas – atomic processes – atomic data – t↗
NASA NTRS2018

A Single Thread to Fortran Coarray Transition Process for the Control Algorithm in the Space Radiation Code HZETRN

Exa-scale computing is the direction by industry and government are going to generate solutions to problems they deem necessary. Computing hardware is being developed to achieve the transition from Peta-scale to Exa-scale with more CPUs (Central Processing Units) that have more cores per CPU and more accelerators (GPGPUs (General Purpose Graphics Processing Units) and MICs (Many Integrated Cores)) per node. To fully utilize the hardware available now and in the future, algorithms must become multi-threaded. There are a few methods to generate multi-threaded software such as MPI (Message Passing Interface) and OpenMP (Multi-Processing) / OpenACC (ACCelerator). This paper concentrates on using Coarray Fortran to convert the Fortran 95 based HZETRN (High Z and Energy TRaNsport) code's control algorithm from a single threaded code to a multithreaded code. The resultant Coarray code was 32.5 times faster (with a theoretical speed-up of 74.5 times) than the single threaded version on the hardware tested, as reliable as the Fortran 95 version, and, as it uses native Fortran, was as maintainable as the Fortran 95 version. The Coarray code can be maintained by the same project engineers and scientists who created the original single threaded code. This transition process can be utilized on a C language based code with a compiler that has the UPC (Universal Parallel C) extensions to C.

Singleterry, Robert C., Jr.↗
DOE OSTI2022

Modernization efforts for the R -Matrix code SAMMY [Abstract]

The R-Matrix code SAMMY is a widely used nuclear data evaluation code focused on the resolved range, which includes corrections for experimental effects. The code is still mostly written in Fortran 77, and uses a memory management system suitable for the time of its initial writing (1984). A modernization effort is under way to bring the code in-line with modern software development practices. A continuous-integration testing framework was added, automating the large existing set of test cases. It is run on every commit. The memory management was updated to current standard practices suitable for modern software analysis tools. The code can be obtained from https://code.ornl.gov/RNSD/SAMMY. The resonance parameters and covariance information are now stored in C++ objects shared by SAMMY and AMPX, the processing code that generates nuclear data libraries for SCALE. This allows for easier maintenance and access to the resonance parameters inside and outside of SAMMY. This feature is already used by accessing and changing parameters in memory in the Bayesian Monte Carlo Evaluation Framework for Cross Sections Nuclear Data and Integral Benchmark Experiments project, Further plans include the switch to the ENDF reading and writing routines in AMPX, as these routines are more robust, easier to maintain, and support more features. Of note here is support for the new GNDS format. Previously it wasn’t easy to share the full covariance matrix for evaluations containing more than one isotope due to limitations on the ENDF format; this is now supported in GNDS. The data are currently available in a binary SAMMY format and can be exported to GNDS to make them more widely available and sharable. The next step will be to use the same resonance processing code at 0K in AMPX and SAMMY as one of the available Reich-Moore R-Matrix formalism. The first step toward this goal is to isolate the reconstruction into a module that takes resonance parameters as its input and does not depend on SAMMY global parameters. This goal has been achieved and it should now be possible to more easily change the resonance formalism and add enhancements as the Phenomenological R-Matrix parameterization of direct, doorway, and compound nuclear reactions discussed elsewhere on this conference. This concerted modernization and enhancement effort provides multiple advantages to the nuclear data community. It will allow parameter optimization using enhanced formalisms, including experimental effects, that better match complex experimental data. Then those evaluated parameters can immediately be passed off to AMPX to be reconstructed with the exact same cross section model and be put into a data library for subsequent testing using SCALE and the Valid Benchmark suite or other suitable benchmark suites.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

An Overview of Material Models in the BISON Fuel Performance Code

BISON is a modern finite element-based nuclear fuel performance code that has been under development at Idaho National Laboratory (INL) since 2009. The code is applicable to both steady and transient fuel behavior and supports the use of one-, two-, and three-dimensional meshes. BISON is designed to be a multi-fuels code. Although primarily applied to Light Water Reactor (LWR) fuel to date, the code has been used to analyze TRISO-coated particle fuel and metal fuel in rod and plate form, design and interpret fuel irradiation experiments and investigate novel fuel concepts. Nuclear fuel operates in an extreme environment that induces complex multiphysics phenomena occurring over distances ranging from inter-atomic spacing to meters, and times scales ranging from microseconds to years. To simulate this behavior requires a wide variety of material models which are often complex and nonlinear. Nearly all of the material models currently available in BISON are empirical, using correlations from existing fuel performance codes or material property libraries. Although these models perform adequately under many conditions, they have well-understood limitations. One obvious weakness is that the models are only valid in the domain of the associated experimental data, and extrapolating beyond this domain can result in substantial errors. A further weakness is that these models are often correlated in terms of imprecise quantities, such as burnup. Materials can, for example, reach a given burnup under very different circumstances, leading to very different material behavior. To overcome these weaknesses, efforts are underway with BISON to develop models based on a multi-scale approach, where material behavior is described with a series of interdependent microstructure based models. This paper provides an overview of the material models available in BISON. To keep the scope manageable, only LWR fuel will be considered. The first section focuses on UO{sub 2} fuel, identifying the models generally required and briefly describing those that have been implemented in the code. The second section repeats this approach for Zircaloy cladding. A final section provides examples of areas where multi-scale material modeling has been applied to BISON. BISON is a modern 2D and 3D nuclear fuel performance code that is applicable to multiple fuel forms. A wide variety of complex and nonlinear material models are required to simulate fuel behavior. Focusing on UO{sub 2} fuel and Zircaloy cladding (LWR fuel), the set of empirical models currently implemented in BISON have been reviewed. To overcome some of the deficiencies associated with empirical models, multi-scale material models are being developed. Two multi-scale models that have been used in BISON were reviewed. (authors)

36 MATERIALS SCIENCE↗
DOE OSTI2016

SE2-ANL Subchannel Analysis with New Heating Calculation Based on VARIANT Transport Code

The multi-assembly, steady-state sub-channel analysis code SE2-ANL has been widely used in thermal-hydraulic analysis of sodium cooled fast reactors (SFR). It is used to compute the core-wide temperature profiles for a given flow distribution and to determine the assembly flow rates yielding a desired (assembly-wise) peak temperature distribution. It is a modified version of SUPERENERGY-2 coupled with the DIF3D/GAMSOR/DIF3D procedure for coupled neutron and gamma heating calculations, developed at Argonne National Laboratory (ANL). In the current version of SE2-ANL, the neutron and gamma fluxes are calculated using the finite-difference diffusion theory option of the DIF3D code with six triangular meshes per hexagonal assembly. In addition, the pin power distributions are estimated by assuming that the power distribution within an assembly is separable in the radial and axial directions. Furthermore, the total heat generation rate in an assembly duct wall is simply determined by a user-specified fraction of the total gamma heating within that assembly. In order to determine the pin power distributions more accurately by eliminating these limitations, a new coupled heating calculation procedure has recently developed based on the neutron and gamma transport calculations with the VARIANT code. For this, the GAMSOR code has been extended to generate the intra-nodal gamma source distribution to be consistent with the trial functions of VARIANT. Using the computed neutron and gamma flux distributions, the power distribution in each fuel pin and duct wall is determined using a new utility code CURVE, which has been developed to evaluate the VARIANT flux solution at the center of each fuel pin and along the duct mid-wall. For each pin segment contained in a VARIANT node, the axial power shape is represented as a quadratic profile. The SE2-ANL code has been modified to interface with the new, coupled neutron and gamma heating calculation scheme. In addition, several improvements have been made on the computational methods and models of SE2-ANL. To eliminate the limit on the axial mesh size due to the numerical instability problem of the current explicit scheme, the numerical scheme for discretizing the energy equation in the axial direction has been changed to the {theta}-method of the SLTHEN code. An automated flow allocation scheme has also been implemented in SE2-ANL to determine assembly flow rates such that the peak cladding mid-wall temperatures of individual orifice zones are equalized over the burn cycle. The impacts of the new heating calculation scheme based on VARIANT transport solutions on the cladding and fuel temperatures have been tested against the existing method of SE2-ANL. Using the existing and new heating calculation schemes, full-core subchannel analyses were performed for the metal core design of the 1000 MWt Advanced Burner Reactor (ABR-1000), and the resulting coolant, cladding and fuel temperatures were compared. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Magic State Distillation using Asymptotically Good Codes on Qudits

Qudits offer the potential for low-overhead magic state distillation, although previous results for asymptotically good codes have required qudit dimension $q\gg 100$ or code length $\mathcal{N}\gg 100$. These parameters far exceed experimental demonstrations of qudit platforms, and thus motivate the search for better codes. Using a novel lifting procedure, we construct the first family of good triorthogonal codes on the $\mathbb{F}_{2^{2m}}$ alphabet with $m \geq 3$ that lies above the Tsfasman-Vladut-Zink bound. These codes yield a family of asymptotically good quantum codes with transversal CCZ gates, enabling constant space overhead magic state distillation with qudit dimension as small as $q=64$. Further, we identify a promising code with parameters $[[42,14,6]]_{64}$. Finally, we show that a distilled $|{CCZ}\rangle_{2^{2m}}$ can be reduced to a $|{CCZ}\rangle_{2^n}$ state for arbitrary $n$ with a constant-depth Clifford circuit of at most 9 computational basis measurements, 12 single-qudit and 9 two-qudit Clifford gates.

Cervia, Michael J. [Washington U., Seattle] (ORCID↗
DOE OSTI2026

Efficient Routing of Quantum LDPC Codes on Programmable 2D Toric Architectures

Quantum low-density parity-check codes are promising candidates towards scalable fault-tolerant quantum computation. Among these, bivariate bicycle (BB) codes offer superior encoding rates and large code distance compared to surface codes. However, their requirement on long-range stabilizer measurements poses significant challenges for implementation on realistic hardware with limited connectivity, such as superconducting circuit platforms. In this work, we introduce a novel hardware-software co-design that leverages a programmable communication network architecture to address these limitations. Our approach utilizes a 2D toric network of oscillators as a flexible communication fabric linking qubits at each site. Such architecture significantly reduces the number of long-range couplers required from O ( n ) to O (√ n ). Dual-rail qubits, along with native gates including Swap-Wait-Swap gates and beamsplitter SWAPs, ensure that long-range two-qubit gates can be executed with high fidelity and low latency. To further enhance performance, our qubit layout and routing algorithm utilize symmetries of the codes and enable maximum parallelism for long-range two-qubit gates, maintaining a low syndrome extraction cycle duration and scalability over the code length. We perform circuit-level simulation with realistic noise modeling based on experimental hardware parameters, observing an logical error rate per logical qubit per cycle of 3.06% for [[18,4,4]] BB code, 2.6× less than the existing experimental result. These findings provide a practical roadmap and identify key technological advancements needed to achieve low-overhead fault-tolerant quantum computing at scale.

Liu, Kun [Yale Univ., New Haven, CT (United States↗
DOE OSTI2018

The international implications of national and local coordination on building energy codes: Case studies in six cities

Building energy efficiency is an important strategy for reducing greenhouse gas emissions globally. In fact, 55 countries have included building energy efficiency in their Nationally Determined Contributions (NDCs) under the Paris Agreement. This research uses building energy code implementation in six cities across different continents as case studies to assess what it may take for countries to implement the ambitions of their energy efficiency goals. Specifically, we look at the cases of Bogota, Colombia; Da Nang, Vietnam; Eskisehir, Turkey; Mexico City, Mexico; Rajkot, India; and Tshwane, South Africa, all of which are “deep dive” cities under the Sustainable Energy for All's Building Efficiency Accelerator. The research focuses on understanding the baseline with existing gaps in implementation and coordination. The methodology used a combination of surveys on code status and interviews with stakeholders at the local and national level, as well as review of published documents. We looked at code development, implementation, and evaluation. The cities are all working to improve implementation, however, the challenges they currently face include gaps in resources, capacity, tools, and institutions to check for compliance. Better coordination between national and local governments could help improve implementation, but that coordination is not yet well established. For example, all six of the cities reported that there was little to no involvement of local stakeholders in development of the national code; only one city reported that it had access to national funding to support code implementation. More robust coordination could better link cities with capacity building and funding for compliance, and ensure that the code reflects local priorities. By understanding gaps in implementation, it can also help in designing more targeted interventions to scale up energy savings.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2017

A Spherical Active Coded Aperture for 4π Gamma-ray Imaging

Gamma-ray imaging facilitates the efficient detection, characterization, and localization of compact radioactive sources in cluttered environments. Fieldable detector systems employing active planar coded apertures have demonstrated broad energy sensitivity via both coded aperture and Compton imaging modalities. But, planar configurations suffer from a limited field-of-view, especially in the coded aperture mode. In order to improve upon this limitation, we introduce a novel design by rearranging the detectors into an active coded spherical configuration, resulting in a 4pi isotropic field-of-view for both coded aperture and Compton imaging. This work focuses on the low- energy coded aperture modality and the optimization techniques used to determine the optimal number and configuration of 1 cm 3 CdZnTe coplanar grid detectors on a 14 cm diameter sphere with 192 available detector locations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Group Ring Ideals Related to Reed–Muller Codes

Reed–Muller codes are one of the most well-studied families of codes; however, there are till open problems regarding their structure. Recently a new ring-theoretic approach has emerged that provides a rather intuitive construction of these codes. This approach is centered around the notion of basic Reed–Muller codes. It is known that basic Reed–Muller codes ℳ{sub π}(m, k) over a prime field are powers of the radical RS of a corresponding group algebra and over a nonprime field there are no such equalities, except for trivial ones. In this paper, we consider the ideals ℜ{sub S}ℳ{sub π}(m, k) that arise while studying the inclusions of the basic codes and radical powers.

97 MATHEMATICS AND COMPUTING↗