Towards the Gibbs Characterization of a Class of Quaternary Bent Functions

2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL) Pub Date : 2017-05-01 DOI:10.1109/ISMVL.2017.39

R. Stankovic, M. Stankovic, J. Astola, C. Moraga

引用次数: 2

Abstract

Bent functions generalized to the alphabet Zq, the ring of integers modulo q, are interesting not just in the realm of multiple-valued functions, but have some applications in the binary environment. The case q = 4, i.e., quaternary bent functions, are of a particular interest due to a simple relationship to binary functions. We consider the possibilities for characterization of quaternary bent functions in terms of the Gibbs derivatives defined with respect to the Reed-Muller-Fourier (RMF) transform for q-valued functions. It is shown that quaternary bent functions can be split into classes of functions sharing the same values for their Gibbs derivatives.

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一类四元弯曲函数的吉布斯刻划

广义到字母Zq的弯曲函数，即以q为模的整数环，不仅在多值函数领域中很有趣，而且在二进制环境中也有一些应用。情况q = 4，即，四元弯曲函数，是特别感兴趣的，由于一个简单的关系，二进制函数。我们考虑了用关于q值函数的Reed-Muller-Fourier (RMF)变换的Gibbs导数来表征四元弯曲函数的可能性。证明了四元弯曲函数可以被划分为具有相同吉布斯导数值的函数类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)

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