On Completely Regular Codes
J. Borges, J. Rif\`a, V. A. Zinoviev
TL;DR
This survey paper reviews the properties, relations, and constructions of completely regular codes, discusses their existence problems, and presents new results on codes with covering radius 2 and extended codes.
Contribution
It provides a comprehensive overview of completely regular codes and introduces new findings on codes with covering radius 2 and extended codes.
Findings
New results on completely regular codes with covering radius 2
New results on extended completely regular codes
Discussion on the existence problem of these codes
Abstract
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are established. In particular, we present a few new results on completely regular codes with covering radius 2 and on extended completely regular codes.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research