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arXiv · 0907.3348

New Binomial Bent Function over the Finite Fields of Odd Characteristic

Tor Helleseth·Alexander Kholosha
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Abstract

The $p$-ary function $f(x)$ mapping $\mathrm{GF}(p^{4k})$ to $\mathrm{GF}(p)$ given by $f(x)={\rm Tr}_{4k}\big(x^{p^{3k}+p^{2k}-p^k+1}+x^2\big)$ is proven to be a weakly regular bent function and the exact values of its Walsh transform coefficients are found. The proof is based on a few new results in the area of exponential sums and polynomials over finite fields that may also be interesting as independent problems.

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Tor Helleseth, Alexander Kholosha. 2009-07-20. New Binomial Bent Function over the Finite Fields of Odd Characteristic. https://arxiv.org/abs/0907.3348

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