New Extremal Binary Self-Dual Codes of Length 72 from M6(F2)G - Group Matrix Rings by a Hybrid Search Technique Based on a Neighbourhood-Virus Optimisation Algorithm
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Tarih
2021
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info:eu-repo/semantics/openAccess
Özet
In this paper, a new search technique based on the virus optimisation algorithm is proposed for calculating the neighbours of binary self-dual codes. The aim of this new technique is to calculate neighbours of self-dual codes without reducing the search field in the search process (this is a known in the literature approach due to the computational time constraint) but still obtaining results in a reasonable time (significantly faster when compared to the standard linear computational search). We employ this new search algorithm to the well-known neighbour method and its extension, the kth-range neighbours and search for binary [72,36,12] self-dual codes. In particular, we present six generator matrices of the form [I36 | τ6(v)], where I36 is the 36×36 identity matrix, v is an element in the group matrix ring M6(F2)G and G is a finite group of order 6, which we then employ to the proposed algorithm and search for binary [72,36,12] self-dual codes directly over the finite field F2. We construct 1471 new Type I binary [72,36,12] self-dual codes with the rare parameters γ=11,13,14,15,17,19,20,21,22,23,25,26,28,29,30,31,32 in their weight enumerators.
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self-dual codes, linear codes, neighbour method, virus optimization algorithm
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Korban, A., Şahinkaya, S. ve Üstün, D. (2021). New Extremal Binary Self-Dual Codes of Length 72 from M6(F2)G - Group Matrix Rings by a Hybrid Search Technique Based on a Neighbourhood-Virus Optimisation Algorithm, arXiv:2109.06522 (2021).
