Partial Spread and Vectorial Generalized Bent Functions

2015/11/05 by Thor Martinsen, Wilfried Meidl, Martinsen, Thor +3
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1511.01705

Abstract

In this paper we generalize the partial spread class and completely describe it for generalized Boolean functions from \F₂ⁿ to ℤ_2^t. Explicitly, we describe gbent functions from \F₂ⁿ to ℤ_2^t, which can be seen as a gbent version of Dillon's PS_ap class. For the first time, we also introduce the concept of a vectorial gbent function from \F₂ⁿ to \Z_q^m, and determine the maximal value which m can attain for the case q=2^t. Finally we point to a relation between vectorial gbent functions and relative difference sets.

Related

• Bent functions generalizing Dillon's partial spread functions
• Full characterization of generalized bent functions as (semi)-bent\n spaces, their dual, and the Gray image
• More characterizations of generalized bent function in odd characteristic, their dual and the gray image
• Bent and \mathbb Z_2^k-bent functions from spread-like partitions
• Generalized bent functions and their Gray images