Abstract
In this work, we use 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 γ=8 in their W68,2 and 40 with γ=9 in their W68,2. These examples are the first in the literature for these γ values. This completes the theoretical list of possible values for γ in W68,2.
Original language | English (US) |
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Article number | 101727 |
Journal | Finite Fields and Their Applications |
Volume | 67 |
DOIs | |
State | Published - Oct 2020 |
Keywords
- Distance of self-dual codes
- Extremal self-dual codes
- Neighbor
- Weight enumerator
- kth neighbor
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- General Engineering
- Applied Mathematics