An extension of an inequality by Ahlswede, El Gamal and Pang for pairs of binary codes
type: Item
instance of: scholarly article
title: An extension of an inequality by Ahlswede, El Gamal and Pang for pairs of binary codes
zbMATH Open document ID: 0576.94017
DOI: 10.1016/S0012-365X(85)80008-X
author: Ph. Piret
author: Philippe Delsarte
published in: Discrete Mathematics
publication date: 1985-01-01T00:00:00Z
review text: \textit{R. Ahlswede, A. El Gamal} and \textit{K. F. Pang} [Discrete Math. 49, 1-5 (1984; Zbl 0532.94013)] proved that if A, B are binary codes of length n such that the Hamming distance between codewords of A and B has a constant value, then the product of the cardinalities of A and B is at most \(2^ n\) when n is even and \(2^{n-1}\) if n is odd. This paper proves the same result by assuming that the distance taken modulo 4 has a constant value. The proof is based on a lemma which states that if the codes A and B satisfy the above mentioned property, then the translated codes \(A+a_ 0\) and \(B+b_ 0\) are orthogonal for any vectors \(a_ 0\) in A and \(b_ 0\) in B. (Two codes A and B are said to be orthogonal if the inner product (x,y) vanishes for all vectors x in A and y in B.)
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 3922528
zbMATH Keywords: orthogonal codes
zbMATH Keywords: product of the cardinalities
MaRDI profile type: Publication
cites work: A two-family extremal problem in Hamming space
cites work: Unrestricted codes with the Golay parameters are unique
full work available at URL: s0012-365x(85)80008-x
OpenAlex ID: W2022772864
description: scientific article; zbMATH DE number 3922528