Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes

Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

“…Recently, one can find in the literature some papers where the above formula (or formulae derived from it) are used for determining the entanglement corresponding to EAQECCs over arbitrary finite fields (see, for instance [6,9,17,21]). Although it holds for any finite field, we have found no proof in the literature and, thus, this work fills this gap.…”

An application of constacyclic codes to entanglement-assisted quantum MDS codes

“…However, the construction given in Theorems 3 and 4 is different from their construction, since q ≡ 3 (mod4) for our construction. Liu et al (2018) derived two classes of EAQMDSCs with the parameters…”

“…Moreover, the definition of Z δ implies that −q Z δ ∩ Z δ = ∅, and by Lemma 1, C ⊥ h δ ⊆ C δ . We have the following result from Liu et al (2018) and .…”

“…In Chen et al (2017), by taking advantage of a decomposition of the defining sets of negacyclic codes, Jianzhang Chen et al determine the number of entanglement states of EAQECCs obtained from negacyclic codes over F q 2 . Then, this result is extended to constacyclic codes over F q 2 in Liu et al (2018) and . For a constacyclic code C over F q 2 with defining set Z , define the sets…”

“…Proposition 2 (Liu et al 2018;) Let C be a constacyclic code over F q 2 with length n and defining set Z , where (n, q) = 1, and let Z = Z β ∪ Z δ be a decomposition of Z . Then, the number c of entanglement states required for EAQECCs obtained from C is equal to |Z β |.…”