On Quadratic Vectorial Bent Functions in Trace Forms

• Published in: Chinese Journal of Electronics Vol. 29; no. 5; pp. 865 - 872
• Main Authors: Zhou, Junchao, Xu, Yunge, Zhang, Wanshan
• Format: Journal Article
• Language: English
• Published: Published by the IET on behalf of the CIE 01.09.2020
• Subjects: Bent function; Extended affine equivalence; Linearized permutation polynomial; Linearized permutation polynomial; Bent function; Extended affine equivalence
• ISSN: 1022-4653; 2075-5597
• DOI: 10.1049/cje.2020.08.001

By permutation behavior of certain linearized polynomials, the bentness of quadratic vectorial bent functions of the form $F(x)=\sum\limits_{i = 1}^{k - 1} {{\rm Tr}_m^n \lpar c_ix^{1 + 2^{it}}\rpar + } {\rm Tr}_m^{kt} \lpar c_kx^{1 + 2^{kt}}\rpar$F(x)=∑i=1k−1Trmn(cix1+2it)+Trmkt(ckx1+2kt) is investigated, where n = 2kt and m | kt with k, t being positive integers. The numerical results show that there exist new quadratic vectorial bent functions obtained up to extended affine equivalence.