New Quantum Codes from Skew Constacyclic Codes Over a Class Of Non-Chain Rings Re, q

Quantum codes from constacyclic codes over $S_{k}$

“…In Table 1, we provide some new quantum codes [[n, l, d]] q (in the sixth column) and compare the constructed codes [[n , l , d ]] q (in the seventh column) better (by means of larger code rate or larger distance) than the existing references [13,16,17]. Further, the [[48, 30, 3]] 9 [16] first column represents the length n, the second column is parameter k for S k , the third column gives the value of units (λ 1 , . .…”

“…Wang et al [15] studied quantum codes over F q from Hermitian dual-containing constacyclic codes over F q 2 + vF q 2 . Prakash et al [16] obtained quantum codes from skew constacyclic codes over a class of non-chain rings R e,q = F q [u]/ u e -1 by applying the CSS construction. Ashraf et al [17] constructed quantum codes from F q R 1 R 2 -cyclic codes and introduced a Gray map to find some new and better quantum codes over F p .…”

Quantum Codes Obtained from Skew ϱ - λ -Constacyclic Codes over R

“…, v l ]/ 〈v 2 i − 1, v i v j − v j v i 〉 1 ≤ i,j ≤ l by using the Hermitian construction. In [24,25], some new quantum codes were obtained from skew constacyclic codes over R e,q [u]/〈u e � 1〉, and some MDS quantum codes were construed from skew cyclic codes over F q [u]/〈u k+1 − u〉 by applying the CSS construction. Dinh et al [26] obtained some optimal codes and near-optimal codes from skew θ-cyclic codes and discussed the advantages of quantum codes from skew θ-cyclic codes than from cyclic codes over F q .…”

Quantum and LCD codes from Skew Constacyclic Codes over a General Class of Non-chain Rings

“…Further a rectified version of this criterion was introduced by Bag et al in [11]. Quantum codes have been constructed from skew constacyclic codes over various finite rings and mixed algebras in [10,11,28,29,52,64,[73][74][75]. Linear Complementary Dual(LCD) codes are an important class of linear codes that were first introduced by Massay [59] in 1992.…”