New Extremal binary self-dual codes of length 68 from a novel approach to neighbors

2020/02/24 by Gildea, Joe, Kaya, Abidin, Korban, Adrian +1
#94B05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.10030

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.

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