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.
Publié le : 2017-02-17
Classification:
extremal self-dual codes, codes over rings, Gray maps, Kharaghani array, extension theorems,
94B05, 94B99
@article{mc1727,
author = {Kaya, Abidin},
title = {New extremal binary self-dual codes of length 68 via short Kharaghani array over F\_2 + uF\_2},
journal = {Mathematical Communications},
volume = {22},
number = {1},
year = {2017},
pages = { 123-133},
language = {eng},
url = {http://dml.mathdoc.fr/item/mc1727}
}
Kaya, Abidin. New extremal binary self-dual codes of length 68 via short Kharaghani array over F_2 + uF_2. Mathematical Communications, Tome 22 (2017) no. 1, pp. 123-133. http://gdmltest.u-ga.fr/item/mc1727/