A class of exponential sums and sequence families

Chengju Li; Qin Yue; Yongbo Xia; Wei Peng

doi:10.1007/s12095-019-00368-4

A class of exponential sums and sequence families

Chengju Li
, Qin Yue
, Yongbo Xia
, Wei Peng^*

^*Corresponding author for this work

Software Engineering Institute

Xidian University
Nanjing University of Aeronautics and Astronautics
South-Central University for Nationalities
East China Normal University

Research output: Contribution to journal › Article › peer-review

Abstract

Let m₁ and m₂ be two distinct positive integers with d= gcd (m₁, m₂). Let F2m be the finite field with 2^m elements, where m = m₁m₂/d. In this paper, we investigate the exponential sumsS(a,b)=∑x∈F2m∗(−1)Trm1(ax2m−12m1−1)+Trm2(bx2m−12m2−1), where a∈F2m1, b∈F2m2, and Tr_t denotes the trace function from F2t to F₂. When d = 1, 2, 3, 4, we present the value distribution of the exponential sums S(a, b) explicitly. As an application, we construct three families of binary sequences with three-valued correlation.

Original language	English
Pages (from-to)	569-584
Number of pages	16
Journal	Cryptography and Communications
Volume	12
Issue number	3
DOIs	https://doi.org/10.1007/s12095-019-00368-4
State	Published - 1 May 2020

Keywords

Character sum
Correlation
Gauss sum
Sequence

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10.1007/s12095-019-00368-4

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title = "A class of exponential sums and sequence families",

abstract = "Let m1 and m2 be two distinct positive integers with d= gcd (m1, m2). Let F2m be the finite field with 2m elements, where m = m1m2/d. In this paper, we investigate the exponential sumsS(a,b)=∑x∈F2m∗(−1)Trm1(ax2m−12m1−1)+Trm2(bx2m−12m2−1), where a∈F2m1, b∈F2m2, and Trt denotes the trace function from F2t to F2. When d = 1, 2, 3, 4, we present the value distribution of the exponential sums S(a, b) explicitly. As an application, we construct three families of binary sequences with three-valued correlation.",

keywords = "Character sum, Correlation, Gauss sum, Sequence",

author = "Chengju Li and Qin Yue and Yongbo Xia and Wei Peng",

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doi = "10.1007/s12095-019-00368-4",

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TY - JOUR

T1 - A class of exponential sums and sequence families

AU - Li, Chengju

AU - Yue, Qin

AU - Xia, Yongbo

AU - Peng, Wei

PY - 2020/5/1

Y1 - 2020/5/1

N2 - Let m1 and m2 be two distinct positive integers with d= gcd (m1, m2). Let F2m be the finite field with 2m elements, where m = m1m2/d. In this paper, we investigate the exponential sumsS(a,b)=∑x∈F2m∗(−1)Trm1(ax2m−12m1−1)+Trm2(bx2m−12m2−1), where a∈F2m1, b∈F2m2, and Trt denotes the trace function from F2t to F2. When d = 1, 2, 3, 4, we present the value distribution of the exponential sums S(a, b) explicitly. As an application, we construct three families of binary sequences with three-valued correlation.

AB - Let m1 and m2 be two distinct positive integers with d= gcd (m1, m2). Let F2m be the finite field with 2m elements, where m = m1m2/d. In this paper, we investigate the exponential sumsS(a,b)=∑x∈F2m∗(−1)Trm1(ax2m−12m1−1)+Trm2(bx2m−12m2−1), where a∈F2m1, b∈F2m2, and Trt denotes the trace function from F2t to F2. When d = 1, 2, 3, 4, we present the value distribution of the exponential sums S(a, b) explicitly. As an application, we construct three families of binary sequences with three-valued correlation.

KW - Character sum

KW - Correlation

KW - Gauss sum

KW - Sequence

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U2 - 10.1007/s12095-019-00368-4

DO - 10.1007/s12095-019-00368-4

M3 - 文章

AN - SCOPUS:85066051237

SN - 1936-2447

VL - 12

SP - 569

EP - 584

JO - Cryptography and Communications

JF - Cryptography and Communications

IS - 3

ER -

A class of exponential sums and sequence families

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Keywords

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