New non-binary quantum codes from skew constacyclic and additive skew constacyclic codes
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Cited by 7 publications
References 41 publications
Let R k = F q u 1 , u 2 , ⋯ , u k / < u i 2 = α i u i , u i u j = u j u i = 0 > , where q = p m , p is an odd prime, α i is a unit over F q , and i , j = 1,2 , ⋯ , k . In this article, we define a Gray map from R k n to F q k + 1 n , we study the structure of skew ϱ - λ -constacyclic codes over R k , and then we give the necessary and sufficient conditions for skew ϱ - λ -constacyclic codes over R k to satisfy dual containing. Further, we have obtained some new nonbinary quantum codes from skew ϱ - λ -constacyclic over R k by using the CSS construction.
Let R k = F q u 1 , u 2 , ⋯ , u k / < u i 2 = α i u i , u i u j = u j u i = 0 > , where q = p m , p is an odd prime, α i is a unit over F q , and i , j = 1,2 , ⋯ , k . In this article, we define a Gray map from R k n to F q k + 1 n , we study the structure of skew ϱ - λ -constacyclic codes over R k , and then we give the necessary and sufficient conditions for skew ϱ - λ -constacyclic codes over R k to satisfy dual containing. Further, we have obtained some new nonbinary quantum codes from skew ϱ - λ -constacyclic over R k by using the CSS construction.
Quantum and LCD codes from Skew Constacyclic Codes over a General Class of Non-chain Rings
In this paper, we study skew constacyclic codes over a class of non-chain rings $\mathcal{T}=\mathbb{F}_q[u_1,u_2,\ldots, u_r]/ \langle f_i(u_i), u_iu_j-u_ju_i\rangle_{i,j=1}^r$, where $q=p^m$, $p$ is some odd prime, $m$ is a positive integer and $f_i(u_i)$ are non-constant polynomials which split into distinct linear factors. We discuss the structural properties of skew constacyclic codes over $\mathcal{T}$ and their dual. We characterize (Euclidean and Hermitian) dual-containing skew constacyclic codes. These characterizations serve as a foundational framework for the development of techniques to construct quantum codes. Consequently, we derive plenty of new quantum codes including many Maximum Distance Separable (MDS) quantum codes, and many quantum codes with better parameters than existing ones. Our work further extends to the characterization of skew constacyclic Euclidean and Hermitian Linear Complementary Dual (LCD) codes over $\mathcal{T}$, and we establish that their Gray images also preserve the LCD property. From this analysis, we derive numerous Maximum Distance Separable (MDS) codes and Best-Known Linear Codes (BKLC) over $\mathbb{F}_q$. MSC Classification: MSC 11T06, MSC 81P70, MSC94B05, MSC 94B15, MSC 94B99
New Quantum Codes from the Images of Cyclic Codes
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