Quantum codes from cyclic codes over F₃+ μF₃+ υF₃+ μυ F₃

Quantum Codes Obtained through Constacyclic Codes over Z3 + νZ3 + ωZ3 + νωZ3

“…Now, let K be a 1 + ν + ω + 2νω-constacyclic code over the ring = Z 3 + νZ 3 + ωZ 3 + νωZ 3 where ν 2 = 1, ω 2 = 1 and νω = ων of length 3. Let g 1 (t) = g 2 (t) = g 3 (t) = t + 1 and g 4 (t) = t 2 +t+1 then g(t) = ξ 1 (t+1)+ξ 2 (t+1)+ξ 3 (t+1)+ξ 4 (t 2 +t+1) be the generator polynomial of K. Since g i (t)g * i (t)|t 3 + 1 for i = 1, 2, 3 respectively and g 4 (t)g * 4 (t)|t 3 − 1, then by the use of Theorem 4.11, we get K ⊥ ⊆ K Further ϕ(K) is a linear code over the ring Z 3 having parameters [12,7,3]. Then, by the application of Theorem 4.18, we obtain the quantum code having parameters [12, 2, ≥ 3] 3 .…”

“…Ashraf and Mohammad [1] gave a construction of quantum codes from cyclic codes overF 3 + vF 3 where v 2 = 1. In 2016, Ozen et al [12] examined several ternary quantum codes from the cyclic codes over F 3 + uF 3 + vF 3 + uvF 3 . Very recently, several researchers established a number of new quantum codes via F p from the classical cyclic and constacyclic codes to which we refer [2,6,[9][10][11]15].…”

On the quantum codes over Yq

“…The skew cyclic codes over were studied. For , the commutative ring was introduced by Mehmet Ozen et al in [14]. In this paper the quantum codes over were constructed by using cyclic codes over .…”

“…Many quantum error correcting codes have been constructed by using classical error correcting codes over many finite rings [3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

New quantum codes from constacyclic codes over the ring $ R_{k,m} $

“…Meantime, Dertli et al [8] presented some new binary quantum codes obtained from the cyclic codes over F 2 + uF 2 + vF 2 + uvF 2 , and then Ashraf and Mohammad [2] generalized their work over the ring F q + uF q + vF q + uvF q to derive new non-binary quantum codes. There are a lot of articles in which good quantum codes are obtained from the cyclic codes on different finite rings, see [11,13,19,23,31,33,32,34]. On the other side, recently, Gao and Wang [12], Li et al [27], Ma et al [29,30] considered the constacyclic codes over finite non-chain rings and obtained many new and better codes compare to the known codes.…”