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Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications

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  • Hongju Li
  • Ping Yu
  • Jing Liang
  • Feng Zhao
  • Jie Wu

Abstract

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.

Suggested Citation

  • Hongju Li & Ping Yu & Jing Liang & Feng Zhao & Jie Wu, 2022. "Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications," Journal of Mathematics, Hindawi, vol. 2022, pages 1-11, February.
    • Handle: RePEc:hin:jjmath:6108863
    DOI: 10.1155/2022/6108863
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