Some new binary codes with improved minimum distances

Year 2018, , 65 - 70, 13.03.2018

Eric Zhi Chen

https://doi.org/10.13069/jacodesmath.404964

Abstract

It has been well-known that the class of quasi-cyclic (QC) codes contain many good codes. In this paper, a method to conduct a computer search for binary $2$-generator QC codes is presented, and a large number of good $2$-generator QC codes have been obtained. $5$ new binary QC codes that improve the lower bounds on minimum distance are presented. Furthermore, with new $2$-generator QC codes and Construction X, $2$ new improved binary linear codes are obtained. With the standard construction techniques, another $16$ new binary linear codes that improve the lower bound on the minimum distance have also been obtained.

Keywords

Binary linear codes, Quasi-cyclic codes, Algorithms

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