TITLE: Polynomial Functions Over Finite Fields AUTHORS: John Hull FACULTY SPONSOR:
نویسنده
چکیده
Introduction: Polynomial functions over finite fields are important in computer science and electrical engineering in that they present a mathematical representation of digital circuits. The validity of circuit designs can be tested abstractly using polynomial representations of circuits instead of physical testing the circuits post-construction. Toward this end, we aim to find necessary and sufficient conditions for polynomial functions with coefficients in a field of characteristic p, when restricted to a subfield, to map from the restricted domain to a different subfield of the original field. This problem is of particular interest in the aforementioned context when p = 2 due to the relationship between fields of characteristic 2 and binary structures.
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