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Computer Science > Information Theory

arXiv:2109.00908 (cs)
[Submitted on 2 Sep 2021]

Title:Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours

Authors:Joe Gildea, Adrian Korban, Adam Michael Roberts, Alexander Tylyshchak
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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.
Comments: arXiv admin note: substantial text overlap with arXiv:2108.09184, arXiv:2106.12355, arXiv:2102.10354
Subjects: Information Theory (cs.IT); Combinatorics (math.CO)
MSC classes: 94B05, 15B10, 15B33
Cite as: arXiv:2109.00908 [cs.IT]
  (or arXiv:2109.00908v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2109.00908
Related DOI: https://doi.org/10.3934/amc.2022021

Submission history

From: Adam Michael Roberts [view email]
[v1] Thu, 2 Sep 2021 13:05:53 UTC (15 KB)
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