Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications - Hongju Li; Ping Yu; Jing Liang; Feng Zhao (Journal of Mathematics)
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.