Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications
Cyclic codes play a very important role in the history of coding theory since they have good algebraic structures that can be widely used in coding and decoding. However, generators for repeated-root cyclic codes of arbitrary length over Fpmu/uk are not unique in previous works for k≥3, and hence it...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6108863 |
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| _version_ | 1832550935865327616 |
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| author | Hongju Li Ping Yu Jing Liang Feng Zhao |
| author_facet | Hongju Li Ping Yu Jing Liang Feng Zhao |
| author_sort | Hongju Li |
| collection | DOAJ |
| description | Cyclic codes play a very important role in the history of coding theory since they have good algebraic structures that can be widely used in coding and decoding. However, generators for repeated-root cyclic codes of arbitrary length over Fpmu/uk are not unique in previous works for k≥3, and hence it is impossible to determine their dual codes. In this work, we propose unique generators for cyclic codes of arbitrary length over Fpmu/u3. As its applications, we derive the numbers of their codewords, as well as generators for their dual codes. Furthermore, we propose necessary and sufficient conditions for their self-dualities. |
| format | Article |
| id | doaj-art-cebe1e3858c1481e8b3fa15525bf1d74 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-cebe1e3858c1481e8b3fa15525bf1d742025-02-03T06:05:31ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/6108863Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their ApplicationsHongju Li0Ping Yu1Jing Liang2Feng Zhao3Department of Liberal EducationDepartment of Liberal EducationDepartment of Liberal EducationDepartment of Liberal EducationCyclic codes play a very important role in the history of coding theory since they have good algebraic structures that can be widely used in coding and decoding. However, generators for repeated-root cyclic codes of arbitrary length over Fpmu/uk are not unique in previous works for k≥3, and hence it is impossible to determine their dual codes. In this work, we propose unique generators for cyclic codes of arbitrary length over Fpmu/u3. As its applications, we derive the numbers of their codewords, as well as generators for their dual codes. Furthermore, we propose necessary and sufficient conditions for their self-dualities.http://dx.doi.org/10.1155/2022/6108863 |
| spellingShingle | Hongju Li Ping Yu Jing Liang Feng Zhao Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications Journal of Mathematics |
| title | Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications |
| title_full | Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications |
| title_fullStr | Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications |
| title_full_unstemmed | Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications |
| title_short | Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications |
| title_sort | unique generators for cyclic codes of arbitrary length over fpmu u3 and their applications |
| url | http://dx.doi.org/10.1155/2022/6108863 |
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