Self-dual bent sequences for complex Hadamard matrices

Self-dual bent sequences for complex Hadamard matrices Full article

Journal

Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586

Output data

Year: 2023, Volume: 91, Number: 4, Pages: 1453-1474 Pages count : 22 DOI: 10.1007/s10623-022-01157-6

Tags

Bent sequences, Complex Hadamard matrices, Regular complex Hadamard matrices, Bush-type complex Hadamard matrices, Mixed-skew Hadamard matrices

Authors

Shi M. ¹ , Li Y. ¹ , Cheng W. ² , Crnković D. ³ , Krotov D. ⁴ , Solé P. ⁵

Affiliations

1	School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
2	Télécom of Paris, Secure-IC University S.A.S., 104 Boulevard du Montparnasse, 75014 Paris, France
3	Faculty of Mathematics, University of Rijeka, Rijeka, Croatia
4	Sobolev Institute of Mathematics, Novosibirsk, Russia, 630090
5	CNRS, University of Aix Marseille, Centrale Marseille, I2M, Marseille, France

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0017

A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application (Solé et al. 2021). In this paper we introduce the analogous notion for complex Hadamard matrices, and we study the self-dual class in length at most 90. We use three competing methods of generation: Brute force, Linear Algebra and Groebner bases. Regular complex Hadamard matrices and Bush-type complex Hadamard matrices provide many examples. We introduce the strong automorphism group of complex Hadamard matrices, which acts on their associated self-dual bent sequences. We give an efficient algorithm to compute that group. We also answer the question which complex Hadamard matrices can be uniquely reconstructed from the off-diagonal elements, define a related concept of mixed-skew Hadamard matrix, and show the existence of mixed-skew Hadamard matrices of small orders.

Shi M. , Li Y. , Cheng W. , Crnković D. , Krotov D. , Solé P.
Self-dual bent sequences for complex Hadamard matrices
Designs, Codes and Cryptography. 2023. V.91. N4. P.1453-1474. DOI: 10.1007/s10623-022-01157-6 WOS Scopus РИНЦ OpenAlex

Submitted:	Apr 25, 2022
Accepted:	Nov 9, 2022
Published online:	Dec 12, 2022
Published print:	Apr 20, 2023

Web of science:	WOS:000899060100002
Scopus:	2-s2.0-85143845516
Elibrary:	59841260
OpenAlex:	W4310858567

DB	Citing
Scopus	2
Web of science	2
OpenAlex	2