Ternary perfect sequences with three-valued cross-correlation

Chenchen Liu; Wenyi Zhang; Yang Yang

doi:10.3934/amc.2022071

Article Contents

2022, Volume 16, Issue 4: 893-901. Doi: 10.3934/amc.2022071

This issue Previous Article A class of minimum storage cooperative regenerating codes with low access property Next Article Optimal data placements for triple replication in distributed storage systems

Ternary perfect sequences with three-valued cross-correlation

1.
University of Science and Technology of China, Hefei, China
2.
Huawei Technologies Corporation Ltd., Shenzhen, China
3.
Southwest Jiaotong University, Chengdu, China

Corresponding author: Wenyi Zhang
Corresponding author: Wenyi Zhang

Received: March 2022

Revised: June 2022

Early access: September 2022

Published: November 2022

The work of Y. Yang was supported in part by the National Science Foundation of China (NSFC) under Grants 62171389

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Abstract

The calculation of the cross-correlation between a sequence with good autocorrelation and its decimated sequence has been a longstanding research problem in the field of sequence design. The objective of this paper is to determine the cross-correlation between a class of well-known ternary sequences with perfect autocorrelation and its $ 2 $-decimation. Based on the theory of quadratic forms and exponential sums over finite fields, it is shown that the cross-correlation function takes on three low values.

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Mathematics Subject Classification: Primary: 94A05, 60G35.

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References

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