Constructing error-correcting binary codes using transitive permutation groups

2016/04/20 by Antti Laaksonen, Laaksonen, Antti, Patric R. J. Östergård +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.CO #math.IT

paper · pdf · doi:10.48550/arxiv.1604.06022

arxiv created 2016/07/18 · arxiv updated 2016/07/19

Abstract

Let A₂(n,d) be the maximum size of a binary code of length n and minimum distance d. In this paper we present the following new lower bounds: A₂(18,4) ≥ 5632, A₂(21,4) ≥ 40960, A₂(22,4) ≥ 81920, A₂(23,4) ≥ 163840, A₂(24,4) ≥ 327680, A₂(24,10) ≥ 136, and A₂(25,6) ≥ 17920. The new lower bounds are a result of a systematic computer search over transitive permutation groups.

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