Akademik Veri Yönetim Sistemi
Second International Bilateral Workshop on Science between Dokuz Eylül University and Azerbaijan National Academy of Science, İzmir, Türkiye, 18 Kasım 2022, ss.27
A binary linear code C of length n is a subspace of the vector space F2n. The elements of C are called codewords. For a non-zero codeword c in C, the support of c is the set of positions of the coordinates of c which are non-zero. The Hamming weight of c, denoted by wt(c), is the number of elements of support of c. The minimum weight of C, denoted by wt(C), is wt(C) = min{wt(x) : x C\{0} } . A binary linear code is called constant weight code if every non-zero codeword has the same Hamming weight. In this talk we give a construction for the binary linear constant weight codes by using the symmetric difference of the supports of the codewords. Moreover, we give a characterization for the constant weight codes with given parameters in terms of supports of the codewords. The arguments in this characterization lead us to construct binary linear constant weight codes up to permutation equivalence. Finally, we consider the permutation automorphism group a constant weight code and prove that the order of the permutation automorphism group is a multiple of six, for any given constant weight code of the dimension bigger than 2.