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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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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DOI: https://doi.org/10.1007/s10623-016-0207-6