Neighbors, neighbor graphs and invariant rings in coding theory
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910687762055168 |
|---|---|
| author | Chakraborty, Himadri Shekhar Chiari, Williams Miezaki, Tsuyoshi Oura, Manabu |
| author_facet | Chakraborty, Himadri Shekhar Chiari, Williams Miezaki, Tsuyoshi Oura, Manabu |
| contents | In the present paper, we discuss the class of Type III and Type IV codes from the perspectives of neighbors. Our investigation analogously extends the results originally presented by Dougherty [8] concerning the neighbor graph of binary self-dual codes. Moreover, as an application of neighbors in invariant theory, we show that the ring of the weight enumerators of Type II code $d_{n}^{+}$ and its neighbors in arbitrary genus is finitely generated. Finally, we obtain a minimal set of generators of this ring up to the space of degree 24 and genus 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04647 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neighbors, neighbor graphs and invariant rings in coding theory Chakraborty, Himadri Shekhar Chiari, Williams Miezaki, Tsuyoshi Oura, Manabu Combinatorics Group Theory Number Theory Rings and Algebras In the present paper, we discuss the class of Type III and Type IV codes from the perspectives of neighbors. Our investigation analogously extends the results originally presented by Dougherty [8] concerning the neighbor graph of binary self-dual codes. Moreover, as an application of neighbors in invariant theory, we show that the ring of the weight enumerators of Type II code $d_{n}^{+}$ and its neighbors in arbitrary genus is finitely generated. Finally, we obtain a minimal set of generators of this ring up to the space of degree 24 and genus 3. |
| title | Neighbors, neighbor graphs and invariant rings in coding theory |
| topic | Combinatorics Group Theory Number Theory Rings and Algebras |
| url | https://arxiv.org/abs/2411.04647 |