A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929226067738624 |
|---|---|
| author | Harada, Masaaki |
| author_facet | Harada, Masaaki |
| contents | We introduce quaternary modified four $μ$-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four $μ$-circulant Hermitian self-dual codes. We also construct quaternary modified four $μ$-circulant Hermitian self-dual codes having large minimum weights. Two quaternary Hermitian self-dual $[56,28,16]$ codes are constructed for the first time. These codes improve the previously known lower bound on the largest minimum weight among all quaternary (linear) $[56,28]$ codes. In addition, these codes imply the existence of a quantum $[[56,0,16]]$ code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes Harada, Masaaki Information Theory Combinatorics 94B, 05B We introduce quaternary modified four $μ$-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four $μ$-circulant Hermitian self-dual codes. We also construct quaternary modified four $μ$-circulant Hermitian self-dual codes having large minimum weights. Two quaternary Hermitian self-dual $[56,28,16]$ codes are constructed for the first time. These codes improve the previously known lower bound on the largest minimum weight among all quaternary (linear) $[56,28]$ codes. In addition, these codes imply the existence of a quantum $[[56,0,16]]$ code. |
| title | A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes |
| topic | Information Theory Combinatorics 94B, 05B |
| url | https://arxiv.org/abs/2401.15265 |