Ambiguity resistant polynomial matrices Original Research Article

AnN × K (N greater-or-equal, slanted K) ambiguity resistant (AR) matrixG(z) is an irreducible polynomial matrix of sizeN × K over a fieldF such that the equationEG(z) = G(z)V(z) with theE and unknown constant matrix andV(z) an unknown polynomial matrix has only the trivial solutionE = αIN, V(z) = αIK, where α εF.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 studyAR matrices over an infinite fieldF. We discuss the classification ofAR matrices, define their normal forms, find their simplest canonical forms, and characterize all(K + 1) × KAR matrices that are the most interesting matrices in the applications.