New linear codes over GF(7), GF(8) and GF(9) from quasi-cyclic codes and Construction X
Sebastian Cochinescu
原文摘要
We present linear codes with parameters [88,8,64]_7, [90,8,65]_7, [98,7,75]_8, [97,8,72]_8, [44,7,31]_9, [97,8,71]_7, [85,6,67]_8 and [78,8,56]_7. Each has a minimum distance one larger than the lower bound listed in Grassl's tables of best known linear codes; codes with parameters [89,8,64]_7, [96,8,71]_8, [95,8,70]_8, [94,8,69]_8, [77,8,55]_7 and [86,6,68]_8 follow. Seven of the eight codes are obtained from a quasi-cyclic code and a vector that is constant on each block, by Construction X with a repetition code. The remaining one, the [90,8,65]_7 code, is obtained from the first by appending two coordinates. The parameters and all weight counts were obtained by exhaustive enumeration, and a short program that repeats these computations is included.
cs.IT