A (72, 36; 15) box code

Abstract

A (72,36;15) box code is constructed as a 9 x 8 matrix whose columns add to form an extended BCH-Hamming (8,4;4) code and whose rows sum to odd or even parity. The newly constructed code, due to its matrix form, is easily decodable for all seven-error and many eight-error patterns. The code comes from a slight modification in the parity (eighth) dimension of the Reed-Solomon (8,4;5) code over GF(512). Error correction uses the row sum parity information to detect errors, which then become erasures in a Reed-Solomon correction algorithm.