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A class of Niho type four-valued cross-correlation functions between sequences of different periods
Abstract
Determining the cross-correlation distributions between m-sequences and their decimated sequences is an important problem in sequence design. For two positive integers n and k with n=2k, this paper investigates the cross-correlation function between a binary m-sequence {u(t)} of period 2n−1 and its 2gcd(s,k)+1 short-period decimated sequences {u(dt+l)}, where the decimation d=2s/(2s+1)(2k−1)+1 satisfies 1<s<n and v2(s)>v2(k). The cross-correlation function is proved to be four-valued and its value distribution is completely determined. Several previously known binary cross-correlation functions are included in our result as special cases.
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BibTeX
@misc{yao2026class,
title = {{A class of Niho type four-valued cross-correlation functions between sequences of different periods}},
author = {Yao Yao and Yufei Wang and Yongbo Xia and Nian Li and Xiangyong Zeng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34010},
eprint = {2610.34010},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34010},
}
RIS
TY - UNPB
TI - A class of Niho type four-valued cross-correlation functions between sequences of different periods
AU - Yao Yao
AU - Yufei Wang
AU - Yongbo Xia
AU - Nian Li
AU - Xiangyong Zeng
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34010
UR - https://arxiv.org/abs/2610.34010
AB - Determining the cross-correlation distributions between m-sequences and their decimated sequences is an important problem in sequence design. For two positive integers n and k with n=2k, this paper investigates the cross-correlation function between a binary m-sequence {u(t)} of period 2^n−1 and its 2^gcd(s,k)+1 short-period decimated sequences {u(dt+l)}, where the decimation d=2^s/(2^s+1)(2^k−1)+1 satisfies 1<s<n and v_2(s)>v_2(k). The cross-correlation function is proved to be four-valued and its value distribution is completely determined. Several previously known binary cross-correlation functions are included in our result as special cases.
ER -