Abstract: 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 Bierbrauer–Friedman–Potapov lower bound on its size is a completely regular code. (We recall that an algebraic T-design is a set of vertices of a graph whose characteristic function is orthogonal to all eigenfunctions corresponding to 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. (We recall that a diameter-perfect code of distance d is a 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).

Cite: Krotov D.S.
Completely Regular Codes as Optimal Structures
In compilation 2023 XVIII International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY). 2023. – C.82 - 87. DOI: 10.1109/Redundancy59964.2023.10330185 Scopus OpenAlex

Dates:

Published print:	Dec 4, 2023
Published online:	Dec 4, 2023

Identifiers:

Scopus:	2-s2.0-85177770315
OpenAlex:	W4389313749

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