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

Authors: 

Tushar Bag, Hai Q. Dinh, Ashish Kumar Upadhyay, Woraphon Yamaka

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