Designs, Codes and Cryptography

, Volume 83, Issue 1, pp 115–143 | Cite as

On linear codes admitting large automorphism groups

  • Nicola Pace
  • Angelo Sonnino


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 \(\text {PSL}(2,8)\rtimes \text {C}_{3}\).


Linear code Projective space Automorphism Matrix group Permutation decoding 

Mathematics Subject Classification

51E22 20B25 94B35 



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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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesDublin Institute of TechnologyDublin 8Ireland
  2. 2.Dipartimento di Matematica, Informatica ed EconomiaUniversità degli Studi della BasilicataPotenzaItaly

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