Quantum codes from (1+βu)-constacyclic codes over Fp m+uFp m
Soumak Biswas, Maheshanand Bhaintwal · 2020 5th International Conference on Computing, Communication and Security (ICCCS) · 2020
In this paper quantum codes over Fpm are constructed from self-orthogonal (1 + βu)-constacyclic codes of length N = npsover R = Fpm + uFpm , u2= 0, where p is an odd prime, (n, p) = 1, and β is a non-zero element of Fpm. To obtain such quantum codes, the algebraic structure of (1 + βu)-constacyclic codes of length N over R is studied. The structure of their duals is also determined. From the algebraic structures of the (1+βu)-constacyclic codes and their duals over R, self-orthogonal codes over Fpm are obtained as Gray images of self-orthogonal codes over R. Then applying the CalderbankShor-Steane (CSS) construction to these self-orthogonal codes over Fpm, the parameters of the corresponding quantum codes are determined. An example is given to illustrate the results.