MacWilliams Theory over Zk and nu-functions over Lattices
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909591906811904 |
|---|---|
| author | Zheng, Zhiyong Liu, Fengxia Tian, Kun |
| author_facet | Zheng, Zhiyong Liu, Fengxia Tian, Kun |
| contents | Continuing previous works on MacWilliams theory over codes and lattices, a generalization of the MacWilliams theory over $\mathbb{Z}_k$ for $m$ codes is established, and the complete weight enumerator MacWilliams identity also holds for codes over the finitely generated rings $\mathbb{Z}_k[ξ]$. In the context of lattices, the analogy of the MacWilliams identity associated with nu-function was conjectured by Solé in 1995, and we present a new formula for nu-function over the lattices associated with a ternary code, which is rather different from the original conjecture. Furthermore, we provide many counterexamples to show that the Solé conjecture never holds in the general case, except for the lattices associated with a binary code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17589 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MacWilliams Theory over Zk and nu-functions over Lattices Zheng, Zhiyong Liu, Fengxia Tian, Kun Information Theory Continuing previous works on MacWilliams theory over codes and lattices, a generalization of the MacWilliams theory over $\mathbb{Z}_k$ for $m$ codes is established, and the complete weight enumerator MacWilliams identity also holds for codes over the finitely generated rings $\mathbb{Z}_k[ξ]$. In the context of lattices, the analogy of the MacWilliams identity associated with nu-function was conjectured by Solé in 1995, and we present a new formula for nu-function over the lattices associated with a ternary code, which is rather different from the original conjecture. Furthermore, we provide many counterexamples to show that the Solé conjecture never holds in the general case, except for the lattices associated with a binary code. |
| title | MacWilliams Theory over Zk and nu-functions over Lattices |
| topic | Information Theory |
| url | https://arxiv.org/abs/2504.17589 |