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New binary linear codes from quasi-cyclic codes and an augmentation algorithm

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Abstract

Explicit construction of linear codes with best possible parameters is one of the major problems in coding theory. Among all alphabets of interest, the binary alphabet is the most important one. In this work we use a comprehensive search strategy to find new binary linear codes in the well-known and intensively studied class of quasi-cyclic (QC) codes. We also introduce a generalization of an augmentation algorithm to obtain further new codes from those QC codes. Also applying the standard methods of obtaining new codes from existing codes, such as puncturing, extending and shortening, we have found a total of 62 new binary linear codes.

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Authors and Affiliations

  1. Department of Mathematics, Kenyon College, Gambier, OH, 43022, USA

    Nuh Aydin, Nicholas Connolly & John Murphree

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  1. Nuh Aydin
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  2. Nicholas Connolly
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  3. John Murphree
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Correspondence to Nuh Aydin.

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Aydin, N., Connolly, N. & Murphree, J. New binary linear codes from quasi-cyclic codes and an augmentation algorithm. AAECC 28, 339–350 (2017). https://doi.org/10.1007/s00200-017-0327-x

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  • DOI: https://doi.org/10.1007/s00200-017-0327-x

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