Affiliation:
1. Sobolev Institute of Mathematics Novosibirsk Russia
Abstract
AbstractA multifold 1‐perfect code (1‐perfect code for list decoding) in any graph is a set of vertices such that every vertex of the graph is at distance not more than 1 from exactly elements of . In ‐ary Hamming graphs, where is a prime power, we characterize all parameters of multifold 1‐perfect codes and all parameters of additive multifold 1‐perfect codes. In particular, we show that additive multifold 1‐perfect codes are related to special multiset generalizations of spreads, multispreads, and that multispreads of parameters corresponding to multifold 1‐perfect codes always exist.
Funder
Russian Science Foundation
Cited by
1 articles.
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