Original scientific paper

Self-dual codes with an automorphism of order 17

Müberra Gürel orcid.org/0000-0003-4727-1548 ; Safir Company Haznedar Mah. Menderes Cad., Istanbul, Turkey
Nikolay Yankov ; Faculty of Mathematics and Informatics, Shumen University, Bulgaria

Abstract

In this paper we study optimal binary self-dual codes with minimum distance 12 having an automorphism of order 17. We prove that all such codes have parameters [68 + f; 34 + f=2; 12]; f = 0; 2; 4 and automorphism of type 17- (4; f), f = 0; 2; 4 and provide a full classication of these codes. This classication gives: new values b = 17, 153, 170, 187, 221, 255 for = 0 in the weight enumerator W68,2 of [68, 34, 12] codes; new values b = 102, 136, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, and 612 for g = 0 in W70,1 of [70, 35, 12] codes; numerous singly- and doubly-even [72, 36, 12] codes with new parameters in their weight enumerators.

Keywords

Automorphism; Classification; Self-dual code

Hrčak ID:

157710

URI

https://hrcak.srce.hr/157710

Publication date:

16.5.2016.

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