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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |