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

Abstract

© 1997-2012 IEEE. For any odd prime p, and a divisor ℓ of p, we consider Iℓ 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 iϵIℓ Ri, for Ri= Fp[u] (ui+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.