Akademik Veri Yönetim Sistemi
Advances in Mathematics of Communications, cilt.18, sa.4, ss.878-891, 2024 (SCI-Expanded, Scopus)
In this paper, a new search technique based on a 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 technique is known in the literature 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, to which we employ 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.