Properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16

Properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 Abstract. Some properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 are presented for reference purposes. The attached files contain some tab-delimited properties of perfect binary codes of length 15 and extended perfect codes of length 16. Classification of such codes can be found in [1], but unfortunately the list of such codes' properties was not attached to the paper. We acknowledge that such properties had been computated by the authors in [1] and our results are presented for reference purposes only. The attached files are perfect15.txt contains a list of properties of all perfect codes of length 15. The properties are: index of the code in classification [1], rank, dimension of the kernel. perfect16.txt contains a list of properties of all extended perfect codes of length 16. The properties are: index of the code in classification [1], rank, dimension of the kernel. transitive15.txt contains a list of properties of all perfect transitive codes of length 15. The properties are: index of the code in classification [1], rank, dimension of the code's kernel, order of the code's automorphism group, number of codewords of weight 3 in the set C + C, order of the code's symmetry group. transitive16.txt contains a list of properties of all extended perfect transitive codes of length 16. The properties are: index of the code in classification [1], rank, dimension of the code's kernel, order of the code's automorphism group, number of codewords of weight 4 in the set C + C, order of the code's symmetry group. All computations have been carried out by using Magma [2] system.