Computing in GF ( q ) By
نویسندگان
چکیده
This paper gives an elementary deterministic algorithm for completely factoring any polynomial over GF(q), q = p , criteria for the identification of three types of primitive polynomials, an exponential representation for GF(<j) which permits direct rational calculations in GF(q) as opposed to modular arithmetic over GF[p, xl, and a matrix representation for GF(p) which admits computer computations. The third type of primitive polynomial examined permits the given representation of GF(<jr) to display a primitive normal basis over GF(p). The techniques developed require only the usual addition and multiplication of square matrices over GF(p). Partial tables from computer programs based on certain of these results will appear in later papers.
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