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IEEE Transactions on Information Theory
Article . 1995 . Peer-reviewed
License: IEEE Copyright
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Packing radius, covering radius, and dual distance

Authors: Patrick Solé;

Packing radius, covering radius, and dual distance

Abstract

Recently, A. Tietäväinen derived an upper bound on the covering radius of codes as a function of the dual distance. This was generalized to the minimum distance, and to \(Q\)-polynomial association schemes by Levenshtein and Fazakas. Both proofs use a linear programming approach. In this correspondence the author rederives in a simple way known upper bounds on the minimum distance and covering radius of a \(q\)-ary unrestricted code with the zero codeword when the dual distance is known. The main idea is to interpret the Pless identities as equalities between two scalar products on vector spaces of polynomials: those associated with the weight distribution and those associated with the binomial distribution. As a by-product upper bounds on the minimum distance of formally self- dual binary codes are derived.

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Keywords

Bounds on codes, upper bounds, covering radius, \(q\)-ary unrestricted code, Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory, minimum distance, self-dual binary codes

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citations
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!
12
Average
Average
Average
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