A class of exponential sums and sequence families

Let m 1 and m 2 be two distinct positive integers with d = gcd ( m 1 , m 2 ) . Let F 2 m be the finite field with 2 m elements, where m = m 1 m 2 / d . In this paper, we investigate the exponential sums S ( a , b ) = ∑ x ∈ F 2 m ∗ ( − 1 ) Tr m 1 ( a x 2 m − 1 2 m 1 − 1 ) + Tr m 2 ( b x 2 m − 1 2 m 2...

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Bibliographic Details
Published in:Cryptography and communications 2020-05, Vol.12 (3), p.569-584
Main Authors: Li, Chengju, Yue, Qin, Xia, Yongbo, Peng, Wei
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Communications Engineering
Computer Science
Data Structures and Information Theory
Fields (mathematics)
Information and Communication
Mathematics of Computing
Networks
Special Issue on Sequences and Their Applications II
Sums
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Summary:Let m 1 and m 2 be two distinct positive integers with d = gcd ( m 1 , m 2 ) . Let F 2 m be the finite field with 2 m elements, where m = m 1 m 2 / d . In this paper, we investigate the exponential sums S ( a , b ) = ∑ x ∈ F 2 m ∗ ( − 1 ) Tr m 1 ( a x 2 m − 1 2 m 1 − 1 ) + Tr m 2 ( b x 2 m − 1 2 m 2 − 1 ) , where a ∈ F 2 m 1 , b ∈ F 2 m 2 , and Tr t denotes the trace function from F 2 t to F 2 . 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.
ISSN:1936-2447
1936-2455
DOI:10.1007/s12095-019-00368-4