The diametric theorem in Hamming spaces---optimal anticodes
type: Item
instance of: scholarly article
title: The diametric theorem in Hamming spaces---optimal anticodes
zbMATH Open document ID: 0909.05044
author: Levon H. Khachatrian
author: Rudolf Ahlswede
published in: Advances in Applied Mathematics
publication date: 1999-01-12T00:00:00Z
review text: Denote by \({\mathcal H}(n, \alpha)\) the Hamming space of \(n\)-length codewords over an \(\alpha\)-element alphabet. The distance of two words is the number of different components. If \(\alpha =2\) then the codewords naturally coincide with the subsets of an \(n\)-element set, and distances are closely related to the sizes of intersections. A codeword set in \({\mathcal H}(n, \alpha)\) with prescribed diameter is called anticode. The anticodes can be considered as the duals of codes. This paper determines the maximum cardinality of anticodes. The result is based on the seminal result of the authors: The complete intersection theorem for systems of finite sets, Eur. J. Comb. 18, No. 2, 125-136, Art. No. ej950092 (1997; Zbl 0869.05066).
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 1221616
zbMATH Keywords: \(t\)-intersecting set systems
zbMATH Keywords: Erdős-Ko-Rado theorem
zbMATH Keywords: Hamming space
zbMATH Keywords: anticodes
zbMATH Keywords: the complete intersection theorem of Ahlswede and Khachatrian
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
full work available at URL: aama.1998.0588
OpenAlex ID: W1992472342
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DOI: 10.1006/AAMA.1998.0588
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description: scientific article; zbMATH DE number 1221616