Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2023-07-31 , DOI: 10.1016/j.jcta.2023.105790 Minjia Shi , Yuhong Xia , Denis S. Krotov
If S is a transitive metric space, then for any distance-d code C and a set A, “anticode”, of diameter less than d. For every Steiner S system S, we show the existence of a q-ary constant-weight code C of length n, weight k (or ), and distance (respectively, ) and an anticode A of diameter such that the pair attains the code–anticode bound and the supports of the codewords of C are the blocks of S (respectively, the complements of the blocks of S). We study the problem of estimating the minimum value of q for which such a code exists, and find that minimum for small values of t.
中文翻译:
Steiner 系统的一系列直径完美恒重代码
如果S是传递度量空间,则对于任何距离为 d 的代码C和直径小于d的集合A (“反码”) 。对于每个 Steiner S系统S,我们证明存在一个长度为n 、重量为k(或) 和距离(分别,) 和直径的反码A使得这对达到码反码界,并且C的码字的支持是S的块(分别是S的块的补集)。我们研究了估计存在这样的代码的q最小值的问题,并找到了小t值的最小值。