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On linear codes admitting large automorphism groups

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Abstract

Linear codes with large automorphism groups are constructed. Most of them are suitable for permutation decoding. In some cases they are also optimal. For instance, we construct an optimal binary code of length \(n=252\) and dimension \(k=12\) having minimum distance \(d=120\) and automorphism group isomorphic to \(\text {PSL}(2,8)\rtimes \text {C}_{3}\).

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Acknowledgments

N. Pace was supported by the Fundação de Amparo a Pesquisa do Estado de São Paulo (FAPESP), Proc. No. 12/03526-0. A. Sonnino was partially supported by the Italian Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) within the PRIN Project No. 2012XZE22K_006.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland

    Nicola Pace

  2. Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Viale dell’Ateneo Lucano, 10, 85100, Potenza, Italy

    Angelo Sonnino

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  1. Nicola Pace
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Correspondence to Nicola Pace.

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Communicated by C. Mitchell.

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Pace, N., Sonnino, A. On linear codes admitting large automorphism groups. Des. Codes Cryptogr. 83, 115–143 (2017). https://doi.org/10.1007/s10623-016-0207-6

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