Several new constructions of mutually unbiased bases derived from functions over finite fields

被引：3

作者：

Qian, Liqin ^{[1
]}

Cao, Xiwang ^{[1
,2
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Sch Math, Nanjing 211106, Peoples R China

[2] MIIT, Key Lab Math Modelling & High Performance Comp Ai, Nanjing 211106, Peoples R China

来源：

QUANTUM INFORMATION PROCESSING | 2022年 / 21卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Character sum; Weakly regular bent function; Permutation polynomial; Mutually unbiased bases; PN function; BENT FUNCTIONS;

D O I：

10.1007/s11128-022-03636-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A collection B = {B-1, B-2, . . . , B-N} of orthonormal bases of C-K is called mutually unbiased bases if vertical bar <upsilon(i) vertical bar upsilon(j)>vertical bar = 1/root K for all upsilon(i) is an element of B-i, upsilon(i) is an element of B-j and 1 <= i < j <= N. In this paper, we present several new series of mutually unbiased bases constructed by utilizing p-ary weakly regular bent functions, permutation polynomials and PN functions over finite fields. Specifically, we are the first to use weakly regular bent functions to construct MUBs. In addition, we obtain a complete set of MUBs by employing linearized permutation polynomials over finite fields.

引用

页数：15

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