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Journal of Combinatorial Designs
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Multifold 1‐perfect codes

Multifold 1-perfect codes
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 20 May 2024Embargo end date: 01 Dec 2022 English Publisher:WileyJournal:Journal of Combinatorial Designs, volume 32, pages 546-555 (issn: 1063-8539, eissn: 1520-6610, Copyright policy )
Authors: Denis S. Krotov;

doi: 10.1002/jcd.21947 , 10.48550/arxiv.2212.03644

arXiv: 2212.03644

Multifold 1‐perfect codes

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.

Related Organizations
Keywords

FOS: Computer and information sciences, intriguing sets, perfect codes, Distance in graphs, Discrete Mathematics (cs.DM), spreads, Computer Science - Information Theory, Information Theory (cs.IT), multispreads, multiple covering, additive codes, list-decoding codes, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), multifold packing, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 94B05, 94B25, 51E23, Linear codes (general theory), completely regular codes, Computer Science - Discrete Mathematics

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    popularity
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    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Top 10%
Average
Average
Green