Constructing rate 1/p systematic binary quasi-cyclic codes based on the matroid theory
Designs, Codes and Cryptography
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Tables of 1/p and rate (p-1 )/p binary quasi-cyclic (QC) codes that extend previously published results are presented. Many of these codes attain bounds given by T. Verhoeff (1987), who composed a table of bounds on the maximum possible minimum distance of binary linear codes. Many of the codes presented meet or improve these bounds. A best code is considered to be one which has the largest possible minimum distance for the given code dimensions. n and k, and class of error correcting codes. A good code has the maximum known minimum distance for the class of codes. An optimal code is one that achieves the maximum possible minimum distance for a linear code with the same dimensions. Binary power residue codes are found and used to construct QC codes.