Abstract
In this paper, LCD cyclic, self dual and isodual codes over finite chain rings are investigated. It was proven recently that a non-free LCD cyclic code does not exist over finite chain rings. Based on algebraic number theory, we introduce necessary and sufficient conditions for which all free cyclic codes over a finite chain ring are LCD. We have also obtained conditions on the existence of non trivial self dual cyclic codes of any length when the nilpotency index of the maximal ideal of a finite chain ring is even. Further, several constructions of isodual codes are given based on the factorization of the polynomial x n−1 over a finite chain ring.
Original language | English |
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Article number | 101993 |
Number of pages | 25 |
Journal | Finite Fields and Their Applications |
Volume | 79 |
DOIs | |
Publication status | Published - 1 Mar 2022 |
Keywords
- Cyclic codes
- Finite chain rings
- Isodual
- LCD
- Self dual