Abstract
In this work, we introduce new construction methods for self-dual codes using a Baumert–Hall array. We apply the constructions over the alphabets F2 and F4+uF4 and combine them with extension theorems and neighboring constructions. As a result, we construct 46 new extremal binary self-dual codes of length 68, 26 new best known Type II codes of length 72 and 8 new extremal Type II codes of length 80 that lead to new 3−(80,16,665) designs. Among the new codes of length 68 are the examples of codes with the rare γ=5 parameter in W68,2. All these new codes are tabulated in the paper.
Original language | English (US) |
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Pages (from-to) | 74-83 |
Number of pages | 10 |
Journal | Discrete Applied Mathematics |
Volume | 271 |
DOIs | |
State | Published - Dec 1 2019 |
Keywords
- Baumert–Hall array
- Codes over rings
- Extension theorems
- Extremal self-dual codes
- Gray maps
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics