New Extremal Binary Self-Dual Codes of Length 72 from M_6(𝔽_2)G - Group Matrix Rings by a Hybrid Search Technique Based on a Neighbourhood-Virus Optimisation Algorithm
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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 k^th-range neighbours and search for binary [72,36,12] self-dual codes. In particular, we present six generator matrices of the form [I_36 | τ_6(v)], where I_36 is the 36 × 36 identity matrix, v is an element in the group matrix ring M_6(𝔽_2)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 𝔽_2. 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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