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Open Problems in Mathematics and Computational Science

pp 111-126

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Open Problems for Polynomials over Finite Fields and Applications

  • Daniel PanarioAffiliated withSchool of Mathematics and Statistics, Carleton University Email author 

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Abstract

We survey open problems for univariate polynomials over finite fields. We first comment in some detail on the existence and number of several classes of polynomials. The open problems in that part of the survey are of a more theoretical nature. Then, we center on classes of low-weight (irreducible) polynomials. The conjectures here are more practically oriented. Finally, we give brief descriptions of a selection of open problems from several areas including factorization of polynomials, special polynomials (APN functions, permutations), and relations between rational integers and polynomials.