New completely regular q-ary codes based on Kronecker products

Josep Rifà; Victor A. Zinoviev

doi:https://doi.org/10.1109/TIT.2009.2034812

New completely regular q-ary codes based on Kronecker products

Josep Rifà, Victor A. Zinoviev

Research output: Contribution to journal › Article › Research › peer-review

14 Citations (Scopus)

Abstract

For any integer ρ ≥ 1 and for any prime power q, an explicit construction of an infinite family of completely regular (and completely transitive) q-ary codes with d = 3 and with covering radius ρ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius ρ, which are not completely regular, is also given. In both constructions, the Kronecker product is the basic tool that has been used. © 2009 IEEE.

Original language	English
Article number	5361491
Pages (from-to)	266-272
Journal	IEEE Transactions on Information Theory
Volume	56
DOIs	https://doi.org/10.1109/TIT.2009.2034812
Publication status	Published - 1 Jan 2010

Keywords

Completely regular codes
Completely transitive codes
Covering radius
Intersection numbers
Kronecker product
Uniformly packed codes

Access to Document

https://doi.org/10.1109/TIT.2009.2034812

Cite this

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title = "New completely regular q-ary codes based on Kronecker products",

abstract = "For any integer ρ ≥ 1 and for any prime power q, an explicit construction of an infinite family of completely regular (and completely transitive) q-ary codes with d = 3 and with covering radius ρ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius ρ, which are not completely regular, is also given. In both constructions, the Kronecker product is the basic tool that has been used. {\textcopyright} 2009 IEEE.",

keywords = "Completely regular codes, Completely transitive codes, Covering radius, Intersection numbers, Kronecker product, Uniformly packed codes",

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AU - Zinoviev, Victor A.

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N2 - For any integer ρ ≥ 1 and for any prime power q, an explicit construction of an infinite family of completely regular (and completely transitive) q-ary codes with d = 3 and with covering radius ρ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius ρ, which are not completely regular, is also given. In both constructions, the Kronecker product is the basic tool that has been used. © 2009 IEEE.

AB - For any integer ρ ≥ 1 and for any prime power q, an explicit construction of an infinite family of completely regular (and completely transitive) q-ary codes with d = 3 and with covering radius ρ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius ρ, which are not completely regular, is also given. In both constructions, the Kronecker product is the basic tool that has been used. © 2009 IEEE.

KW - Completely regular codes

KW - Completely transitive codes

KW - Covering radius

KW - Intersection numbers

KW - Kronecker product

KW - Uniformly packed codes

U2 - https://doi.org/10.1109/TIT.2009.2034812

DO - https://doi.org/10.1109/TIT.2009.2034812

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M1 - 5361491

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