1. Binary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme.
- Author
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Dougherty, Steven, Korban, Adrian, Șahinkaya, Serap, and Ustun, Deniz
- Subjects
GROUP rings ,CODE generators ,HEURISTIC ,AUTOMORPHISM groups ,FINITE groups - Abstract
We present a generator matrix of the form $ [ \sigma(v_1) \ | \ \sigma(v_2)] $, where $ v_1 \in RG $ and $ v_2\in RH $, for finite groups $ G $ and $ H $ of order $ n $ for constructing self-dual codes and linear complementary dual codes over the finite Frobenius ring $ R $. In general, many of the constructions to produce self-dual codes forces the code to be an ideal in a group ring which implies that the code has a rich automorphism group. Unlike the traditional cases, codes constructed from the generator matrix presented here are not ideals in a group ring, which enables us to find self-dual and linear complementary dual codes that are not found using more traditional techniques. In addition to that, by using this construction, we improve $ 10 $ of the previously known lower bounds on the largest minimum weights of binary linear complementary dual codes for some lengths and dimensions. We also obtain $ 82 $ new binary linear complementary dual codes, $ 50 $ of which are either optimal or near optimal of lengths $ 41 \leq n \leq 61 $ which are new to the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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