We completely determine the explicit generators of cyclic codes of length pk(k≥1) over a Galois ring of characteristic p3 by their residue degree, and their two torsional degrees; there are exactly three types of cyclic codes, that is, one-generator, two-generator and three-generator cyclic codes. Using this classification result, we explicitly obtain a mass formula for cyclic codes of length pk over a Galois ring of characteristic p3.
Bibliographical noteFunding Information:
Supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2017R1A2B2004574). The authors are also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).
- Cyclic code
- Galois ring
- Mass formula