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Generalized bent functions and their Gray images. (English) Zbl 1409.11135
Duquesne, Sylvain (ed.) et al., Arithmetic of finite fields. 6th international workshop, WAIFI 2016, Ghent, Belgium, July 13–15, 2016. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 10064, 160-173 (2016).
Summary: In this paper we prove that generalized bent (gbent) functions defined on $$\mathbb {F}_2^n$$ with values in $$\mathbb {Z}_{2^k}$$ are regular, and show connections between the (generalized) Walsh spectrum of these functions and their components. Moreover, we analyze generalized bent and semibent functions with values in $$\mathbb {Z}_{16}$$ in detail, extending earlier results on gbent functions with values in $$\mathbb {Z}_4$$ and $$\mathbb {Z}_8$$.
For the entire collection see [Zbl 1358.11011].

##### MSC:
 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) 11T06 Polynomials over finite fields 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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