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.
Highlights
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
With the standard construction techniques, another 16 new binary linear codes that improve the lower bound on the minimum distance have been obtained
A binary linear [n, k, d] code is a k-dimensional subspace of GF(2 )n, where n is the block length, k the dimension of the code, and d is the minimum distance between any two codewords
Summary
A binary linear [n, k, d] code is a k-dimensional subspace of GF(2 )n, where n is the block length, k the dimension of the code, and d is the minimum distance between any two codewords. For a given block length n and dimension k, it is desired to have an [n, k, d] code with the minimum distance as large as possible. For small code dimension and block length, it is possible to do exhaustive computer search for optimal codes With the standard code constructions, 16 more codes that improve the minimum distance in [13] are obtained
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