CORRELATION MEASURES OF BINARY SEQUENCES USING ADDITIVE CHARACTERS

被引：0

作者：

Liu, Huaning ^{[1
]}

Ren, Yixin ^{[1
]}

Shen, Wenhui ^{[1
]}

机构：

[1] Northwest Univ, Res Ctr Number Theory & Applicat, Sch Math, Xian 710127, Peoples R China

来源：

COLLOQUIUM MATHEMATICUM | 2024年 / 175卷 / 02期

基金：

中国国家自然科学基金;

关键词：

binary sequence; additive character; correlation measure; exponential sum; LARGE FAMILIES; PSEUDORANDOM; CONSTRUCTION;

D O I：

10.4064/cm9202-4-2024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Mauduit, Rivat and S & aacute;rk & ouml;zy presented a construction of a binary sequence which utilizes properties of additive characters and polynomials, and showed that for this sequence both W(EN) and the correlations of "small" order are "small" if the order of the correlation is less than the degree of the polynomial. They conjectured that if the order of the correlation is greater than the degree of the polynomial, then the correlation is large. We further study the correlation measures of the sequence defined by Mauduit, Rivat and S & aacute;rk & ouml;zy and show that if the polynomial is monic with degree d = 2 alpha - 1 for alpha >= 2 then the correlation of order k = d +1 = 2 alpha is very large.

引用

页码：211 / 220

页数：10

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