Abstract: In this chapter, we present tables of small parameters of completely regular (CR) codes in Hamming graphs H(n, q), q = 2, 3. We list all putative intersection arrays with intersection numbers up to some limit (depending on the covering radius) that pass some basic tests (see Sections 7.1.1, 7.1.2, 7.1.5, 7.1.4) and, for each array A, show the best known lower and upper (if exists) bounds on the smallest n such that an A-CR code exists in H(n, q). The tables are preceded by two auxiliary sections, where we describe known necessary conditions and constructions that are sufficient to build the tables. We should note that some nice families of linear CR codes are not represented in the tables because of large parameters; moreover, first questionable parameters of linear CR codes are rather large (see [40]). So, we can say that our tables are mainly focused on unrestricted CR codes and cannot be considered as a good reference for linear CR codes.

Cite: Koolen J.H. , Krotov D.S. , Martin W.J.
Completely regular codes: tables of small parameters for binary and ternary Hamming graphs
Monography chapter Completely Regular Codes in Distance-Regular Graphs. – Chapman & Hall., 2025. – C.449-502. – ISBN 9781032494449. DOI: 10.1201/9781003393931-7 Scopus OpenAlex

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Published online:

Mar 14, 2025

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Scopus:	2-s2.0-105001312466
OpenAlex:	W4407438019

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