Реферат: We survey several results showing that optimal structures from different classes attaining a specific bound are described as completely regular codes with certain parameters. Examples of such structures are error-correcting codes, orthogonal arrays, edge cuts. We prove two new results of such kind. At first, we prove that in an arbitrary finite regular graph, an algebraic T-design attaining the generalized Bierbrauer-Friedman lower bound on its size is a completely regular code. (An algebraic T-design is a set of vertices whose characteristic function is orthogonal to all eigenfunctions corresponding to the T largest non-main eigenvalues of the graph.) At second, we show that every diameter-perfect code is completely regular in a specially constructed graph. (A diameter-perfect code is a minimum-distance-d code C attaining the code-anticode bound |C|·|A|≤|S|, where S is the finite ambient metric space with transitive group of isometries and A, an anticode, is a set of diameter less than d).

Библиографическая ссылка: Krotov D.
Completely Regular Codes as Optimal Structures
2023 年编码与密码国际研讨会 08-10 Dec 2023