Bounds for self-dual codes over \(\mathbb{Z}_4\)
type: Item
instance of: scholarly article
title: Bounds for self-dual codes over \(\mathbb{Z}_4\)
zbMATH Open document ID: 1011.94030
published in: Finite Fields and their Applications
publication date: 2002-01-06T00:00:00Z
review text: This paper presents new bounds on the minimum Hamming and Lee distances of self-dual codes over \(\mathbb{Z}_4\). For a self-dual code \(C\) of length \(n\), the Hamming weight is bounded by \(H(C) \leq 4[n/24] + f(n \bmod 24)\), for an explicitly given function \(f\). The Lee weight of a code \(C\) is bounded by the simple inequality \(L(C) \leq 2H(C)\), and this is used to obtain the Lee weight bound \(L(C) \leq 8[n/24] + g(n \bmod 24)\), where \(g\) is a function different from \(f\). Over a wide range of lengths, these bounds agree with the linear programming bound. The proof of these bounds relies on bounding the minimum dual distance of a doubly even binary code.
Mathematics Subject Classification ID: 94B65
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 1471639
zbMATH Keywords: \(Z_4\) codes
zbMATH Keywords: weight enumerators
zbMATH Keywords: Lee weight
zbMATH Keywords: bounds
zbMATH Keywords: minimum Hamming distances
zbMATH Keywords: self-dual codes
zbMATH Keywords: Hamming weight
author: Eric Rains
reviewed by: T. Aaron Gulliver
MaRDI profile type: Publication
full work available at URL: ffta.1999.0258
OpenAlex ID: W2064973173
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DOI: 10.1006/FFTA.1999.0258
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description: scientific article; zbMATH DE number 1471639