Ambiguity resistant polynomial matrices

An N x K (N greater than or equal to K) ambiguity resistant (AR) matrix G(z) is an irreducible polynomial matrix of size N x 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 is an element of 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) x K AR matrices that are the most interesting matrices in the applications. (C) 1999 Elsevier Science Inc. All rights reserved.