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Quantum codes from $ \sigma $-dual-containing constacyclic codes over $ \mathfrak{R}_{l, k} $
- Source :
- AIMS Mathematics, Vol 8, Iss 10, Pp 24075-24086 (2023)
- Publication Year :
- 2023
- Publisher :
- AIMS Press, 2023.
-
Abstract
- Let $ \mathfrak{R}_{l, k} = {\mathbb F}_{p^m}[u_1, u_2, \cdots, u_k]/ \langle u_{i}^{l} = u_{i}, u_iu_j = u_ju_i = 0 \rangle $, where $ p $ is a prime, $ l $ is a positive integer, $ (l-1)\mid(p-1) $ and $ 1\leq i, j\leq k $. First, we define a Gray map $ \phi_{l, k} $ from $ \mathfrak{R}_{l, k}^n $ to $ {\mathbb F}_{p^m}^{((l-1)k+1)n} $, and study its Gray image. Further, we study the algebraic structure of $ \sigma $-self-orthogonal and $ \sigma $-dual-containing constacyclic codes over $ \mathfrak{R}_{l, k} $, and give the necessary and sufficient conditions for $ \lambda $-constacyclic codes over $ \mathfrak{R}_{l, k} $ to satisfy $ \sigma $-self-orthogonal and $ \sigma $-dual-containing. Finally, we construct quantum codes from $ \sigma $-dual-containing constacyclic codes over $ \mathfrak{R}_{l, k} $ using the CSS construction or Hermitian construction and compare new codes our obtained better than the existing codes in some recent references.
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 8
- Issue :
- 10
- Database :
- Directory of Open Access Journals
- Journal :
- AIMS Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.96d9eaee7f3f4097b59f26a1443cd17f
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/math.20231227?viewType=HTML