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

Abidin Kaya


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.


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

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ISSN: 1331-0623 (Print), 1848-8013 (Online)