Irreducible polynomials over composite Galois fields and their applications in coding techniques

Abstract

Tables of irreducible polynomials and their exponents are listed for certain small nonprime Galois fields. These include all such polynomials up to and including degree 5 for GF(4), degree 3 for GF(8) and GF(9), and degree 2 for GF(16). In addition, a single primitive polynomial is given for each degree up to and including degree 11 for GF(4), degree 7 for GF(8) and GF(9), and degree 5 for GF(16). A brief summary is given of several areas where these results may prove useful in providing an alternative to the more conventional approach.