Quaternary codes with new parameters from two-generator simplicial complexes
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911685548179456 |
|---|---|
| author | Yadav, Ankit Mondal, Nilay Kumar Sarma, Ritumoni |
| author_facet | Yadav, Ankit Mondal, Nilay Kumar Sarma, Ritumoni |
| contents | In this article, we construct infinite families of quaternary (that is, over the ring $\mathbb{Z}_4$) $\mathcal{C}_{D}$-codes, where the defining set $D$ is derived utilizing a two-generator simplicial complex, and determine their Lee weight distributions. As a result, we find at least 32 new or improved quaternary linear codes as per the database \cite{aydin2022updated} of best-known quaternary codes, including codes from a Plotkin-optimal family. We also report 6 projective quaternary linear codes with best-known parameters that might outperform the currently reported best-known codes due to their projectivity. Further, we establish necessary and sufficient conditions for their Gray image to be linear, which in turn gives an infinite family of Griesmer codes and several infinite families of minimal binary linear codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14603 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quaternary codes with new parameters from two-generator simplicial complexes Yadav, Ankit Mondal, Nilay Kumar Sarma, Ritumoni Information Theory 94B05, 94B25, 94B60, 11T71 In this article, we construct infinite families of quaternary (that is, over the ring $\mathbb{Z}_4$) $\mathcal{C}_{D}$-codes, where the defining set $D$ is derived utilizing a two-generator simplicial complex, and determine their Lee weight distributions. As a result, we find at least 32 new or improved quaternary linear codes as per the database \cite{aydin2022updated} of best-known quaternary codes, including codes from a Plotkin-optimal family. We also report 6 projective quaternary linear codes with best-known parameters that might outperform the currently reported best-known codes due to their projectivity. Further, we establish necessary and sufficient conditions for their Gray image to be linear, which in turn gives an infinite family of Griesmer codes and several infinite families of minimal binary linear codes. |
| title | Quaternary codes with new parameters from two-generator simplicial complexes |
| topic | Information Theory 94B05, 94B25, 94B60, 11T71 |
| url | https://arxiv.org/abs/2605.14603 |