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Designs, Codes and Cryptography

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14-10-2016

Energy bounds for codes and designs in Hamming spaces

Authors: P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin, E. B. Saff, M. M. Stoyanova

Published in: Designs, Codes and Cryptography | Issue 1-2/2017

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Abstract

We obtain universal bounds on the energy of codes and designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow a unified treatment, and can be viewed as a generalization of the Levenshtein bounds for maximal codes.

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Here the point \(-x\) is the unique point in \(\mathbb {H}(n,2)\) such that \(d(x,-x)=n\).

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Title: Energy bounds for codes and designs in Hamming spaces
Authors: P. G. Boyvalenkov
P. D. Dragnev
D. P. Hardin
E. B. Saff
M. M. Stoyanova
Publication date: 14-10-2016
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 1-2/2017
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-016-0286-4

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