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Designs, Codes and Cryptography

Erschienen in:

01.03.2015

Classification of self-dual codes of length 50 with an automorphism of odd prime order

verfasst von: Nikolay Yankov, Moon Ho Lee

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2015

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Abstract

By applying a method for constructing binary self-dual codes with an automorphism of odd prime order \(p\), we give a full classification of all optimal binary self-dual codes of length 50 having an automorphism of order 3. As a consequence, we give a full classification of all \([50, 25, 10]\) codes possessing an automorphism of odd prime order. Up to equivalence, there are exactly 177,601 such codes. This completely determines all possibilities for the cardinality of the automorphism group of such a code. Also, we show that there are at least 52 non-isomorphic quasi-symmetric 2-(49, 9, 6) designs, derived from the \([50,25,10]\) codes with a particular weight enumerator.

Vorheriger Artikel Computing in degree -extensions of finite fields of odd characteristic

Nächster Artikel Paley type sets from cyclotomic classes and Arasu–Dillon–Player difference sets

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Titel: Classification of self-dual codes of length 50 with an automorphism of odd prime order
verfasst von: Nikolay Yankov
Moon Ho Lee
Publikationsdatum: 01.03.2015
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2015
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-013-9874-8

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