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Ars Combinatoria

New binary linear codes

Thomas Aaron Gulliver, Patric R. J. Östergård

Published Jan 1, 2000• 10 citations
OpenAlex

Abstract

In this paper, nineteen new binary linear codes are presented which improve the bounds on the maximum possible minimum distance. These codes belong to the class of quasi-cyclic (QC) codes, and have been constructed using a stochastic optimization algorithm, tabu search. Six of the new codes meet the upper bound on minimum distance and so are optimal.

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In this paper, nineteen new binary linear codes are presented which improve the bounds on the maximum possible minimum distance. These codes belong to the class of quasi-cyclic (QC) codes, and have been constructed using a stochastic optimization algorithm, tabu search. Six of the new codes meet the upper bound on minimum distance and so are optimal.
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 222-generator QC codes is presented, and a large number of good 222-generator QC codes have been obtained. 555 new binary QC codes that improve the lower bounds on minimum distance are presented. Furthermore, with new 222-generator QC codes and Construction X, 222 new improved binary linear codes are obtained. With the standard construction techniques, another 161616 new binary linear codes that improve the lower bound on the minimum distance have also been obtained. Received: 9 November 2016 Accepted: 22 November 2017
In this paper, we introduce a class of dualcontaining 2 -generator quasi-cyclic codes over GF(4)G F(4)GF(4). By Hermitian construction, we show computation constructions of binary quantum codes with good parameters from quaternary quasi-cyclic codes. Furthermore, 3 new quantum codes [[42, 10, 9]], [[74,,36, 9]] and [[78, 40, 9]] are derived from Hermitian dual-containing quasi-cyclic codes by an exhaustive search, along with 24 newly derived codes that enhance the previously best-known lower bounds on minimum distance.