Ambiguity resistant polynomial matrices
type: Item
instance of: scholarly article
title: Ambiguity resistant polynomial matrices
zbMATH Open document ID: 0939.15013
DOI: 10.1016/S0024-3795(98)10127-1
author: Guangcai Zhou
author: X.-G. Xia
published in: Linear Algebra and its Applications
publication date: 2000-07-05T00:00:00Z
review text: An error control code defined over a complex field which maps each \(K\) input samples into \(N\) output samples is called \(N\times K\) code. An \(N \times K\) \((N \geq K)\) ambiguity resistant \((AR)\) matrix \(G(z)\) is an irreducible polynomial matrix of size \(N\times K\) over a field \(F\) such that the equation \(EG(z)= G(z)V(z)\) with \(E\) an unknown constant matrix and \(V(z)\) an unknown polynomial matrix has only the trivial solution \(E=\alpha I_N\), \(V(z)= \alpha I_K\), where \(\alpha\in F\). \(AR\) matrices have been introduced and applied in modern digital communications as error control codes defined over the complex field. In this paper the authors systematically study \(AR\) matrices over an infinite field \(F\). They discuss the classification of \(AR\) matrices, define their normal forms, find their simplest canonical forms, and characterize all \((K+1)\times K\) \(AR\) matrices in the applications. The paper is organized as follows. In Section 2 they present the canonical forms for \(N\times K\) \(AR\) matrices. In Section 3, they provide the necessary and sufficient conditions for a polynomial matrix of size \(N\times (N-1)\) to be \(AR\) in terms of its systematic or canonical form.
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 94B10
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 1331723
zbMATH Keywords: ambiguity resistant matrix
zbMATH Keywords: error control code
zbMATH Keywords: irreducible polynomial matrix
zbMATH Keywords: canonical forms
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1331723