New Extremal binary self-dual codes of length 68 from a novel approach to neighbors
Combinatorics
2020-02-25 v1
Abstract
In this work, we introduce the concept of distance between self-dual codes, which generalizes the concept of a neighbor for self-dual codes. Using the k-neighbors, we are able to construct extremal binary self-dual codes of length 68 with new weight enumerators. We construct 143 extremal binary self-dual codes of length 68 with new weight enumerators including 42 codes with gamma=8 in their W_{68,2} and 40 with gamma=9 in their W_{68,2}. These examples are the first in the literature for these gamma values. This completes the theoretical list of possible values for gamma in W_{68,2}.
Cite
@article{arxiv.2002.10030,
title = {New Extremal binary self-dual codes of length 68 from a novel approach to neighbors},
author = {Joe Gildea and Abidin Kaya and Adrian Korban and Bahattin Yildiz},
journal= {arXiv preprint arXiv:2002.10030},
year = {2020}
}