Self-dual Hadamard bent sequences
Combinatorics
2023-04-28 v2 Information Theory
math.IT
Abstract
A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application ( Sol\'e et al, 2021). We study the self dual class in length at most We use three competing methods of generation: Exhaustion, Linear Algebra and Groebner bases. Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples. We conjecture that if is an even perfect square, a self-dual bent sequence of length always exist. We introduce the strong automorphism group of Hadamard matrices, which acts on their associated self-dual bent sequences. We give an efficient algorithm to compute that group.
Cite
@article{arxiv.2203.16439,
title = {Self-dual Hadamard bent sequences},
author = {Minjia Shi and Yaya Li and Wei Cheng and Dean Crnković and Denis Krotov and Patrick Solé},
journal= {arXiv preprint arXiv:2203.16439},
year = {2023}
}