Original scientific paper
New extremal binary self-dual codes of length 68 via short Kharaghani array over F_2 + uF_2
Abidin Kaya
; Department of Computer Engineering, Bursa Orhangazi University, Yildirim Yerle¸skesi Mimar Sinan Mah., Turkey R
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
Hrčak ID:
176733
URI
Publication date:
4.4.2017.
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