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Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours
Gildea, Joe Korban, Adrian Roberts, Adam Tylyshchak, Alexander
Gildea, Joe
Korban, Adrian
Roberts, Adam
Tylyshchak, Alexander
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2022-04-01
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Abstract
In this work, we define a modification of a bordered construction for self-dual codes which utilises \lambda-circulant matrices. We provide the necessary conditions for the construction to produce self-dual codes over finite commutative Frobenius rings of characteristic 2. Using the modified construction together with the neighbour construction, we construct many binary self-dual codes of lengths 54, 68, 82 and 94 with weight enumerators that have previously not been known to exist.
Citation
Gildea, J., Korban, A., Roberts, A. M., & Tylyshchak, A. (2024). Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours. Advances in Mathematics of Communications, 18(3), 738-75. https://doi.org/10.3934/amc.2022021
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American Institute of Mathematical Sciences
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Advances in Mathematics of Communications
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Article
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This article has been accepted for publication in a revised form in [Advances in Mathematics of Communications] [https://www.aimsciences.org//article/doi/10.3934/amc.2022021]. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works
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ISSN
1930-5346
EISSN
1930-5338