Abstract: Many classes of combinatorial objects can be defined as an exact covering (perhaps with multiplicity) of a given set by special subsets. For such classes, trades are often defined as two col- lections of subsets that cover the same points (with the same multiplicities). However, trades can also be defined for objects that cannot be treated as exact coverings. We discuss several equivalent definitions of trades of extended 1-perfect codes and two nonequivalent definitions of trades of ex- tended nearly perfect 1-covering codes. This is joint work with Evgeny Bespalov, Tuvi Etzion, Minjia Shi, and Wenhao Song.

Cite: Krotov D.
Trades of some codes related to perfect codes
2026 Workshop on Algebraic Combinatorics at Hefei 26-28 Sep 2026