Inequalities for code pairs
type: Item
instance of: scholarly article
title: Inequalities for code pairs
zbMATH Open document ID: 0549.05007
DOI: 10.1016/S0195-6698(88)80044-1
author: Michael Moers
author: Rudolf Ahlswede
published in: European Journal of Combinatorics
publication date: 1988-01-01T00:00:00Z
review text: The main result is the following inequality: If \(A,B\subset \{1,...,\alpha\}^ m\); \(m\in {\mathbb{N}}\); satisfies for the Hamming distance d \(d(a,b)-d(a,b')+d(a',b')-d(a',b)\neq 1,2\) for all \(a,a'\in A\) and \(b,b'\in B\), then \(| A|\;| B|\leq \alpha^{*m}\), where \(\alpha^*=\alpha\) for \(\alpha =2,3,4,\) \(\alpha^*= \frac{\alpha}{2} \frac{\ulcorner\alpha \urcorner}{2}\) for \(\alpha \geq 4\), and the bound is best. It is a generalization of the first author, \textit{A. El Gamal} and \textit{K. F. Pang} [Discrete Math. 49, 1-5 (1984; Zbl 0532.94013)], \textit{P. Delsarte} and \textit{P. Piret} [An extension of an inequality by Ahlswede, El Gamal and Pang for pairs of binary codes, submitted to Discrete Math.]).
Mathematics Subject Classification ID: 05A20
Mathematics Subject Classification ID: 94B99
zbMATH DE Number: 3875291
zbMATH Keywords: code pairs
zbMATH Keywords: Hamming distance
MaRDI profile type: Publication
cites work: A two-family extremal problem in Hamming space
cites work: An extension of an inequality by Ahlswede, El Gamal and Pang for pairs of binary codes
cites work: Q3705357
full work available at URL: s0195-6698(88)80044-1
OpenAlex ID: W2045682744
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description: scientific article; zbMATH DE number 3875291