Ambiguity resistant polynomial matrices

Guangcai Zhou; Xiang Gen Xia

doi:10.1016/S0024-3795(98)10127-1

Ambiguity resistant polynomial matrices

Guangcai Zhou, Xiang Gen Xia^*

^*此作品的通讯作者

University of Delaware

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

An N × K (N ≥ K) ambiguity resistant (AR) matrix G(z) is an irreducible polynomial matrix of size N × 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 = αI_N, V(z) = αI_K, where α ∈ F. AR matrices have been introduced and applied in modern digital communications as error control codes defined over the complex field. In this paper we systematically study AR matrices over an infinite field F. We discuss the classification of AR matrices, define their normal forms, find their simplest canonical forms, and characterize all (K + 1) × K AR matrices that are the most interesting matrices in the applications,

源语言	英语
页（从-至）	19-35
页数	17
期刊	Linear Algebra and Its Applications
卷	286
期	1-3
DOI	https://doi.org/10.1016/S0024-3795(98)10127-1
出版状态	已出版 - 1 1月 1999
已对外发布	是

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Zhou, G., & Xia, X. G. (1999). Ambiguity resistant polynomial matrices. Linear Algebra and Its Applications, 286(1-3), 19-35. https://doi.org/10.1016/S0024-3795(98)10127-1

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author = "Guangcai Zhou and Xia, {Xiang Gen}",

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AB - An N × K (N ≥ K) ambiguity resistant (AR) matrix G(z) is an irreducible polynomial matrix of size N × 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 = αIN, V(z) = αIK, where α ∈ F. AR matrices have been introduced and applied in modern digital communications as error control codes defined over the complex field. In this paper we systematically study AR matrices over an infinite field F. We discuss the classification of AR matrices, define their normal forms, find their simplest canonical forms, and characterize all (K + 1) × K AR matrices that are the most interesting matrices in the applications,

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Ambiguity resistant polynomial matrices

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