Exact 2-divisibility of exponential sums associated to boolean functions

被引：0

作者：

Castro, Francis N. ^{[1
]}

Medina, Luis A. ^{[1
]}

Rubio, Ivelisse M. ^{[2
]}

机构：

[1] Univ Puerto Rico, Dept Math, POB 70377, San Juan, PR 00936 USA

[2] Univ Puerto Rico, Dept Comp Sci, POB 70377, San Juan, PR 00936 USA

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2018年 / 10卷 / 04期

关键词：

2-divisibility; Hamming weight; Exponential sums; Balanced Boolean functions; Reed-Muller codes; P-DIVISIBILITY; CONJECTURE; WEIGHTS;

D O I：

10.1007/s12095-017-0252-7

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we extend the covering method for computing the exact 2-divisibility of exponential sums of Boolean functions, improve results on the divisibility of the Hamming weight of deformations of Boolean functions, and provide criteria to obtain non-balanced functions. In particular, we present criteria to determine cosets of Reed-Muller codes that do not contain any balanced function, and to construct deformations of symmetric functions that are not balanced. The use of the covering method together with classifications of cosets of Reed-Muller codes obtained by the action of linear groups can improve the search of balanced functions in Reed-Muller codes dramatically.

引用

页码：655 / 666

页数：12

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