Generalized bent functions and their Gray images

2015/11/04 by Martinsen, Thor, Meidl, Wilfried, Stanica, Pantelimon
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1511.01438

Abstract

In this paper we prove that generalized bent (gbent) functions defined on ℤ₂ⁿ with values in ℤ_2^k are regular, and find connections between the (generalized) Walsh spectrum of these functions and their components. We comprehensively characterize generalized bent and semibent functions with values in ℤ₁₆, which extends earlier results on gbent functions with values in ℤ₄ and ℤ₈. We also show that the Gray images of gbent functions with values in ℤ_2^k are semibent/plateaued when k=3,4.

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