Construction of Galois fields of characteristic two and irreducible polynomials
J. D. Swift · Mathematics of Computation · 1960
A practical method of constructing Galois fields of characteristic two and simultaneously giving a way of generating large supply of irreducible polynomials was developed. The only problems left by the Galois field structure theorems are those of finding an irreducible polynomial of degree m over the base field and of finding a primitive generator of the field with respect to the polynomial. The primary tool in the investigation was a highspeed routine programmed for SWAC. It was used to find possible generators which were in turn used to produce irreducible polynomials. (M.C.G.)