A survey on maximum distance holey packings
type: Item
instance of: scholarly article
title: A survey on maximum distance holey packings
zbMATH Open document ID: 0995.05032
DOI: 10.1016/S0166-218X(01)00301-8
author: Jianxing Yin
published in: Discrete Applied Mathematics
publication date: 2002-08-29T00:00:00Z
review text: A \(q\)-ary code with length \(n\) and constant Hamming weight \(k\) can be viewed as a design with block size \(k\) on \(n\) groups (or holes) of \(q-1\) points (corresponding to the nonzero coordinate values)---that is, of type \((q-1)^n\). For \(q\geq 3\), a maximum distance holey packing, MDHP\((2,k,n,q-1)\), is such a design that corresponds to an optimal code with minimum distance \(d = 2k-3\). By optimal, the author means a code that attains a Schönheim-type (or Johnson-type) bound. The paper surveys constructions of maximum distance holey packings and known existence results.
Mathematics Subject Classification ID: 05B40
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 94B25
zbMATH DE Number: 1792348
zbMATH Keywords: constant weight code
zbMATH Keywords: generalized Steiner system
zbMATH Keywords: group divisible design
zbMATH Keywords: holey packing
reviewed by: Patric R. J. Östergård
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1792348