The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
En 2017, Tang et al. fourni une caractérisation complète des fonctions courbées généralisées de ℤ2n à ℤq(q = 2m) en termes de fonctions de leurs composants (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). Dans cette lettre, pour un général même q, nous visons à fournir quelques caractérisations et davantage de constructions de fonctions courbées généralisées avec des coefficients flexibles. Tout d’abord, nous présentons quelques conditions suffisantes pour qu’une fonction booléenne généralisée avec au plus trois termes soit courbée. Sur la base de ces résultats, nous donnons une réponse positive à une question restante proposée par Hodžić en 2015. Nous prouvons également que les conditions suffisantes sont également nécessaires dans certains cas particuliers. Toutefois, la question de savoir si ces conditions suffisantes sont également nécessaires reste en général un problème ouvert. Deuxièmement, d’un point de vue uniforme, nous proposons une construction secondaire de la fonction gbent, qui inclut plusieurs constructions connues comme cas particuliers.
Zhiyao YANG
Fujian Normal University
Pinhui KE
Fujian Normal University
Zhixiong CHEN
Putian University
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Copier
Zhiyao YANG, Pinhui KE, Zhixiong CHEN, "Characterization and Construction of Generalized Bent Functions with Flexible Coefficients" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 5, pp. 887-891, May 2022, doi: 10.1587/transfun.2021EAL2079.
Abstract: In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ2n to ℤq(q = 2m) in terms of their component functions (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). In this letter, for a general even q, we aim to provide some characterizations and more constructions of generalized bent functions with flexible coefficients. Firstly, we present some sufficient conditions for a generalized Boolean function with at most three terms to be gbent. Based on these results, we give a positive answer to a remaining question proposed by Hodžić in 2015. We also prove that the sufficient conditions are also necessary in some special cases. However, these sufficient conditions whether they are also necessary, in general, is left as an open problem. Secondly, from a uniform point of view, we provide a secondary construction of gbent function, which includes several known constructions as special cases.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAL2079/_p
Copier
@ARTICLE{e105-a_5_887,
author={Zhiyao YANG, Pinhui KE, Zhixiong CHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Characterization and Construction of Generalized Bent Functions with Flexible Coefficients},
year={2022},
volume={E105-A},
number={5},
pages={887-891},
abstract={In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ2n to ℤq(q = 2m) in terms of their component functions (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). In this letter, for a general even q, we aim to provide some characterizations and more constructions of generalized bent functions with flexible coefficients. Firstly, we present some sufficient conditions for a generalized Boolean function with at most three terms to be gbent. Based on these results, we give a positive answer to a remaining question proposed by Hodžić in 2015. We also prove that the sufficient conditions are also necessary in some special cases. However, these sufficient conditions whether they are also necessary, in general, is left as an open problem. Secondly, from a uniform point of view, we provide a secondary construction of gbent function, which includes several known constructions as special cases.},
keywords={},
doi={10.1587/transfun.2021EAL2079},
ISSN={1745-1337},
month={May},}
Copier
TY - JOUR
TI - Characterization and Construction of Generalized Bent Functions with Flexible Coefficients
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 887
EP - 891
AU - Zhiyao YANG
AU - Pinhui KE
AU - Zhixiong CHEN
PY - 2022
DO - 10.1587/transfun.2021EAL2079
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2022
AB - In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ2n to ℤq(q = 2m) in terms of their component functions (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). In this letter, for a general even q, we aim to provide some characterizations and more constructions of generalized bent functions with flexible coefficients. Firstly, we present some sufficient conditions for a generalized Boolean function with at most three terms to be gbent. Based on these results, we give a positive answer to a remaining question proposed by Hodžić in 2015. We also prove that the sufficient conditions are also necessary in some special cases. However, these sufficient conditions whether they are also necessary, in general, is left as an open problem. Secondly, from a uniform point of view, we provide a secondary construction of gbent function, which includes several known constructions as special cases.
ER -