New Non-Binary Quantum Codes from Cyclic Codes Over Product Rings

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 F_p and F_p S_ℓ , where S_ℓ = Π _i∈Iℓ R_i , for R_i = (Fp[u])/(〈u ⁱ⁺¹ -u〉). For that, first we construct linear codes and a Gray map over R_ℓ . Using this construction, we study cyclic codes over R_ℓ, and then extend that over F_p S_ℓ . We also give a Gray map over F_p S_ℓ . 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.