Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916791837523968 |
|---|---|
| author | Bhowmick, Sanjit Deka, Kuntal Tabue, Alexandre Fotue Martínez-Moro, Edgar |
| author_facet | Bhowmick, Sanjit Deka, Kuntal Tabue, Alexandre Fotue Martínez-Moro, Edgar |
| contents | This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are free modules. Moreover, we present a necessary and sufficient condition for a pair of additive cyclic codes over a finite commutative ring to form an additive complementary pair. Finally, we construct a complementary pair of additive cyclic codes over a finite chain ring and show that one of the codes is permutation equivalent to the trace dual of the other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings Bhowmick, Sanjit Deka, Kuntal Tabue, Alexandre Fotue Martínez-Moro, Edgar Information Theory 94B05, 15B05, 12E10 This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are free modules. Moreover, we present a necessary and sufficient condition for a pair of additive cyclic codes over a finite commutative ring to form an additive complementary pair. Finally, we construct a complementary pair of additive cyclic codes over a finite chain ring and show that one of the codes is permutation equivalent to the trace dual of the other. |
| title | Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings |
| topic | Information Theory 94B05, 15B05, 12E10 |
| url | https://arxiv.org/abs/2506.10381 |