On the factorization of polynomials and direct sum properties in integer polyomial rings

Abstract

In our recent work, we solved the word sequence length constraint problem associated with number theoretic transforms defined in finite integer rings. This is based on the American-Indian-Chinese extension of the Chinese remainder theorem. This work builds further on the results by extending them to the domain of integer polynomial rings. The theory of polynomial factorization and the resulting direct sum property are studied in depth. The emphasis is on the theory of computational algorithms for processing sequences defined in finite integer and complex integer rings.