New extremal binary self-dual codes of length 68 via short Kharaghani array over F_2 + uF_2

Abidin Kaya

Vol. 22 No. 1 (2017)

Regular Articles

New extremal binary self-dual codes of length 68 via short Kharaghani array over F_2 + uF_2

Published 2016-11-12

Abidin Kaya

Abidin Kaya
Bursa Orhangazi University, Bursa, TURKEY

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Abstract

In this work, new construction methods for self-dual codes are given. The methods use the short Kharaghani array and a variation of it. These are applicable to any commutative Frobenius ring. We apply the constructions over the ring F_2 + uF_2 and self-dual Type I [64, 32, 12]2-codes with various weight enumerators obtained as Gray images.By the use of an extension theorem for self-dual codes we were able to construct 27 new extremal binary self-dual codes of length 68. The existence of the extremal binary self-dual codes with these weight enumerators was previously unknown.

Keywords

extremal self-dual codes, codes over rings, Gray maps, Kharaghani array, extension theorems

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Author Biography

Abidin Kaya

Assistant Professor of Mathematics at the department of Computer Engineering, Bursa Orhangazi University.