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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IEEE
2025-01-01
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| 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 |
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| 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%. |
| format | Article |
| id | doaj-art-d46e45f7cfc94bcdbc5ae9922082cf5a |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
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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 |