Ambiguity resistant polynomial matrices

Abstract

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 the E and unknown constant matrix and V(z) an unknown polynomial matrix has only the trivial solution E = αI N , V(z) = αI K , where α ε F . AR martices 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.