$\mathbb{F}_q\mathbb{F}_{q^2}$-additive cyclic codes and their Gray images
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909886053351424 |
|---|---|
| author | Yadav, Ankit Sarma, Ritumoni |
| author_facet | Yadav, Ankit Sarma, Ritumoni |
| contents | We investigate additive cyclic codes over the alphabet $\mathbb{F}_{q}\mathbb{F}_{q^2}$, where $q$ is a prime power. First, its generator polynomials and minimal spanning set are determined. Then, examples of $\mathbb{F}_{q^2}$-additive cyclic codes that satisfy the well-known Singleton bound are constructed. Using a Gray map, we produce certain optimal linear codes over $\mathbb{F}_{3}$. Finally, we obtain a few optimal ternary linear complementary dual (LCD) codes from $\mathbb{F}_{3}\mathbb{F}_{9}$-additive codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{F}_q\mathbb{F}_{q^2}$-additive cyclic codes and their Gray images Yadav, Ankit Sarma, Ritumoni Information Theory We investigate additive cyclic codes over the alphabet $\mathbb{F}_{q}\mathbb{F}_{q^2}$, where $q$ is a prime power. First, its generator polynomials and minimal spanning set are determined. Then, examples of $\mathbb{F}_{q^2}$-additive cyclic codes that satisfy the well-known Singleton bound are constructed. Using a Gray map, we produce certain optimal linear codes over $\mathbb{F}_{3}$. Finally, we obtain a few optimal ternary linear complementary dual (LCD) codes from $\mathbb{F}_{3}\mathbb{F}_{9}$-additive codes. |
| title | $\mathbb{F}_q\mathbb{F}_{q^2}$-additive cyclic codes and their Gray images |
| topic | Information Theory |
| url | https://arxiv.org/abs/2511.02325 |