Self-dual codes using bisymmetric matrices and group rings

Gildea, Joe; Kaya, Abidin; Korban, Adrian; Tylyshchak, Alexander

doi:10.1016/j.disc.2020.112085

Cited by 11 publications

(9 citation statements)

References 16 publications

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“…Numerical results from i-range neighbours. The possible weight enumerator of an extremal binary self-dual code of length 68 (of parameters [68,34,12]) is in one of the following forms by [4,12,6]: Let N (0) be the extremal binary self-dual code of length 68 (W 68,2 ) with the parameters γ = 5 and β = 213 which was recently constructed in [9]. Its binary generating matrix is given by (I 34 |A) where…”

Section: Applications Of K-range Neighbor Codes To Extremal Self-dual...mentioning

confidence: 99%

New Extremal binary self-dual codes of length 68 from a novel approach to neighbors

Gildea¹,

Kaya²,

Korban³

et al. 2020

Preprint

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In this work, we introduce 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 W 68,2 and 40 with γ = 9 in their W 68,2 . These examples are the first in the literature for these γ values. This completes the theoretical list of possible values for γ in W 68,2 .

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Section: Applications Of K-range Neighbor Codes To Extremal Self-dual...mentioning

confidence: 99%

New Extremal binary self-dual codes of length 68 from a novel approach to neighbors

Gildea¹,

Kaya²,

Korban³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…2.4 for more details). Recent applications of this isomorphism in constructing self-dual codes can be seen in [1,8,15,16].…”

Section: Introductionmentioning

confidence: 99%

New binary self-dual codes of lengths 80, 84 and 96 from composite matrices

Gildea

Korban

Roberts

2021

Des. Codes Cryptogr.

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In this work, we apply the idea of composite matrices arising from group rings to derive a number of different techniques for constructing self-dual codes over finite commutative Frobenius rings. By applying these techniques over different alphabets, we construct best known singly-even binary self-dual codes of lengths 80, 84 and 96 as well as doubly-even binary self-dual codes of length 96 that were not known in the literature before.

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“…A substantial amount of work has been done on constructing self-dual codes having an automorphism of odd prime order [36,62,63,[66][67][68]. Recently, a strong connection between group rings and self-dual codes was established [21] which has been utilised to develop a number of different techniques for constructing extremal binary self-dual codes [14,25,30,32].…”

Section: Introductionmentioning

confidence: 99%

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

Gildea¹,

Korban²,

Roberts³

et al. 2021

Preprint

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In this work, we define a modification of a bordered construction for self-dual codes which utilises λ-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.

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Self-dual codes using bisymmetric matrices and group rings

Cited by 11 publications

References 16 publications

New Extremal binary self-dual codes of length 68 from a novel approach to neighbors

New Extremal binary self-dual codes of length 68 from a novel approach to neighbors

New binary self-dual codes of lengths 80, 84 and 96 from composite matrices

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

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