Self-dual [62, 31, 12] and [64, 32, 12] codes with an automorphism of order 7

Nikolay Yankov

doi:10.3934/amc.2014.8.73

Article Contents

2014, Volume 8, Issue 1: 73-81. Doi: 10.3934/amc.2014.8.73

This issue Previous Article Weierstrass semigroup and codes over the curve $y^q + y = x^{q^r + 1}$ Next Article Sets of zero-difference balanced functions and their applications

Self-dual [62, 31, 12] and [64, 32, 12] codes with an automorphism of order 7

Nikolay Yankov^1,

1.
Faculty of Mathematics and Informatics, Konstantin Preslavski University of Shumen, Shumen, 9712

Received: February 2013

Revised: June 2013

Published: February 2014

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Abstract

This paper studies and classifies all binary self-dual $[62, 31, 12]$ and $[64, 32, 12]$ codes having an automorphism of order 7 with 8 cycles. This classification is done by applying a method for constructing binary self-dual codes with an automorphism of odd prime order $p$. There are exactly 8 inequivalent binary self-dual $[62, 31, 12]$ codes with an automorphism of type $7-(8,6)$. As for binary $[64,32,12]$ self-dual codes with an automorphism of type $7-(8,8)$ there are 44465 doubly-even and 557 singly-even such codes. Some of the constructed singly-even codes for both lengths have weight enumerators for which the existence was not known before.

Keywords:

Automorphisms,
self-dual codes.

Mathematics Subject Classification: Primary: 11T71; Secondary: 94B05.

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