English

New extremal binary self-dual codes of length 68 via short kharaghani array over f_2 + uf_2

Combinatorics 2016-02-24 v1 Information Theory math.IT

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

Cite

@article{arxiv.1602.07085,
  title  = {New extremal binary self-dual codes of length 68 via short kharaghani array over f_2 + uf_2},
  author = {Abidin Kaya},
  journal= {arXiv preprint arXiv:1602.07085},
  year   = {2016}
}

Comments

10 pages, 5 tables