Perfect Gaussian Integer Sequences With Two Cycles

The complex sequences including Gaussian integers have received considerable attention in the past due to their wide applications in communications and cryptosystems. This paper proposes three new base sequences along with six known ones to construct two novel classes of perfect Gaussian integer seq...

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Main Authors: Kun-Lin Lee, Chong-Dao Lee, Yan-Haw Chen
Format: Article
Language:English
Published: IEEE 2025-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/11091318/
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author Kun-Lin Lee
Chong-Dao Lee
Yan-Haw Chen
author_facet Kun-Lin Lee
Chong-Dao Lee
Yan-Haw Chen
author_sort Kun-Lin Lee
collection DOAJ
description The complex sequences including Gaussian integers have received considerable attention in the past due to their wide applications in communications and cryptosystems. This paper proposes three new base sequences along with six known ones to construct two novel classes of perfect Gaussian integer sequences (PGISs). The first is two-cycle PGIS, where each Gaussian integer has an absolute value such that these values in a <inline-formula> <tex-math notation="LaTeX">$2p$ </tex-math></inline-formula>-periodic sequence form two cycles of period p. Compared to the conventional PGISs, the computational complexity of determining a two-cycle PGIS is reduced by approximately one-half. The second is zero-deletion PGIS (ZDPGIS) when the resulting shorter PGIS is obtained from a long even-length PGIS by deleting zero elements. Experimental results show that the shorter PGISs have flexible lengths including odd and even, most of which are either optimal or almost optimal two-cycle. Such ZDPGISs outperform conventional ones in reducing the computational complexity up to 62.5%.
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spelling doaj-art-d46e45f7cfc94bcdbc5ae9922082cf5a2025-08-20T03:58:41ZengIEEEIEEE Access2169-35362025-01-011313087213088210.1109/ACCESS.2025.359197611091318Perfect Gaussian Integer Sequences With Two CyclesKun-Lin Lee0Chong-Dao Lee1https://orcid.org/0000-0003-0305-084XYan-Haw Chen2Department of Electrical and Computer Engineering, Tamkang University, New Taipei City, TaiwanDepartment of Information Engineering, I-Shou University, Kaohsiung City, TaiwanDepartment of Information Engineering, I-Shou University, Kaohsiung City, TaiwanThe complex sequences including Gaussian integers have received considerable attention in the past due to their wide applications in communications and cryptosystems. This paper proposes three new base sequences along with six known ones to construct two novel classes of perfect Gaussian integer sequences (PGISs). The first is two-cycle PGIS, where each Gaussian integer has an absolute value such that these values in a <inline-formula> <tex-math notation="LaTeX">$2p$ </tex-math></inline-formula>-periodic sequence form two cycles of period p. Compared to the conventional PGISs, the computational complexity of determining a two-cycle PGIS is reduced by approximately one-half. The second is zero-deletion PGIS (ZDPGIS) when the resulting shorter PGIS is obtained from a long even-length PGIS by deleting zero elements. Experimental results show that the shorter PGISs have flexible lengths including odd and even, most of which are either optimal or almost optimal two-cycle. Such ZDPGISs outperform conventional ones in reducing the computational complexity up to 62.5%.https://ieeexplore.ieee.org/document/11091318/Autocorrelationbase sequencesperfect Gaussian integer sequences (PGISs)two-cycle
spellingShingle Kun-Lin Lee
Chong-Dao Lee
Yan-Haw Chen
Perfect Gaussian Integer Sequences With Two Cycles
IEEE Access
Autocorrelation
base sequences
perfect Gaussian integer sequences (PGISs)
two-cycle
title Perfect Gaussian Integer Sequences With Two Cycles
title_full Perfect Gaussian Integer Sequences With Two Cycles
title_fullStr Perfect Gaussian Integer Sequences With Two Cycles
title_full_unstemmed Perfect Gaussian Integer Sequences With Two Cycles
title_short Perfect Gaussian Integer Sequences With Two Cycles
title_sort perfect gaussian integer sequences with two cycles
topic Autocorrelation
base sequences
perfect Gaussian integer sequences (PGISs)
two-cycle
url https://ieeexplore.ieee.org/document/11091318/
work_keys_str_mv AT kunlinlee perfectgaussianintegersequenceswithtwocycles
AT chongdaolee perfectgaussianintegersequenceswithtwocycles
AT yanhawchen perfectgaussianintegersequenceswithtwocycles