New Absolute Irreducibility Testing Criteria and Factorization of Multivariate Polynomials

In this chapter, we introduce a new concept of degree-gap of a multivariate polynomial. We effectively utilize this concept to present a bound on the number of absolutely irreducible factors of an infinite family of multivariate polynomials. We also show how this result can be used to guarantee that a polynomial is absolutely irreducible. We also present an algorithm for testing the absolute irreducibility of multivariate polynomials over finite fields. We discuss the ramifications and applications of our results to algebraic geometry, coding theory, cryptography, finite geometry, and other research domains.