Walter Berge: Constructing a Groebner basis for a bent function without Buchbergers algorithm

Abstract

In this paper we study a particular bent function (as defined by Rothaus in 1975) from a Groebner basis perspective. By generating an ideal from the chosen bent function in conjunction with a set of polynomials limiting the variety to Z_2^n we construct Groebner bases algorithmically in various dimensions and analyze them to find a pattern. From this pattern we construct a set of polynomials which we then prove to be a Groebner basis for this ideal. It is possible that other bent functions have Groebner bases that can be described in this way which may lead toward a general classification of bent functions.

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