TY - JOUR
T1 - A class of exponential sums and sequence families
AU - Li, Chengju
AU - Yue, Qin
AU - Xia, Yongbo
AU - Peng, Wei
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
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
UR - https://www.scopus.com/pages/publications/85066051237
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 -