Divisors of codes of Reed-Muller type
type: Item
instance of: scholarly article
title: Divisors of codes of Reed-Muller type
zbMATH Open document ID: 0801.94014
DOI: 10.1016/0012-365X(94)90392-1
author: Harold N. Ward
published in: Discrete Mathematics
publication date: 1994-08-29T00:00:00Z
review text: Let \(F\) denote the finite field \(GF(q)\) where \(q\) is a power of the prime \(p\). The exponent of a linear code over \(F\) is the exponent of the highest power of \(p\) that divides all the codeword weights. It is shown how to compute the exponents of codes in a class that includes radical powers in group algebras of arbitrary \(p\)-groups. The computation involves the solution of the combinatorial bin-packing problem, known to be NP-complete. For some groups, including Abelian groups, it is shown that certain standard algorithms for this problem produce optimal solutions and yield the exact exponent.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 16K20
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 626337
zbMATH Keywords: error-correcting codes
zbMATH Keywords: Reed-Muller codes
zbMATH Keywords: ideals
zbMATH Keywords: group algebras
reviewed by: Ian Blake
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 626337