New Non-Binary Quantum Codes from Cyclic Codes Over Product Rings
New Non-Binary Quantum Codes from Cyclic Codes Over Product Rings
Source title:
IEEE Communications Letters, 24(3): 486-490,
2020
(ISI)
Academic year of acceptance:
2020-2021
Abstract:
For any odd prime p, and a divisor ℓ of p, we consider Ie to be the set of all divisors of p - 1, which are less than or equal to ℓ. In this letter, we construct quantum codes from cyclic codes over Fp and Fp Sℓ , where Sℓ = Π i∈Iℓ Ri , for Ri = (Fp[u])/(〈u i+1 -u〉). For that, first we construct linear codes and a Gray map over Rℓ . Using this construction, we study cyclic codes over Rℓ, and then extend that over Fp Sℓ . We also give a Gray map over Fp Sℓ . Then, using necessary and sufficient condition of dual containing property for cyclic codes, we construct quantum MDS codes. It is observed that the quantum codes constructed are new in the literature.