Full characterization of generalized bent functions as (semi)-bent\n spaces, their dual, and the Gray image

2016/05/18 by Samir Hodžić, Wilfried Meidl, Hodžić, Samir +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Chromatin Remodeling and Cancer #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Peptidase Inhibition and Analysis

paper · pdf · doi:10.48550/arxiv.1605.05713

openalex publication_date 2016/05/18 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In difference to many recent articles that deal with generalized bent (gbent)\nfunctions f:\ℤ₂ⁿ \→ \ℤ_q for certain small valued\nq\∈ 4,8,16 , we give a complete description of these functions for both\nn even and odd and for any q=2^k in terms of both the necessary and\nsufficient conditions their component functions need to satisfy. This enables\nus to completely characterize gbent functions as algebraic objects, namely as\naffine spaces of bent or semi-bent functions with interesting additional\nproperties, which we in detail describe. We also specify the dual and the Gray\nimage of gbent functions for q=2^k. We discuss the subclass of gbent\nfunctions which corresponds to relative difference sets, which we call\n\ℤ_q-bent functions, and point out that they correspond to a class of\nvectorial bent functions. The property of being \ℤ_q-bent is much\nstronger than the standard concept of a gbent function. We analyse two examples\nof this class of functions.\n

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