New Binomial Bent Function over the Finite Fields of Odd Characteristic

Details New Binomial Bent Function over the Finite Fields of Odd Characteristic New Binomial Bent Function over the Finite Fields of Odd Characteristic

2009-07-20

arxiv.org/abs/0907.3348v1

Computer Science

Discrete Mathematics

13 pages

Scientific paper

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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