A study of QECCs and EAQECCs construction from cyclic codes over the ring 𝔽_q+v_1𝔽_q+v_2𝔽_q+⋯ +v_s𝔽_q

In this paper, we present a construction of quantum error-correcting codes (QECCs) codes and entanglement-assisted quantum error-correcting (EAQECCs) using Euclidean hulls and sums of cyclic codes of length n over a family of ring R_s = 𝔽_q+v_1𝔽_q+v_2𝔽_q+⋯ +v_s𝔽_q , where q is an odd prime power and v_i ^2=v_i , v_iv_j=v_jv_i=0 , for i,j= 1,2,3,⋯ ,s and i j . The study delves into various aspects of this construction. We explore the generator polynomials, the dimension of both Euclidean hulls and the sums of cyclic codes over the ring R_s . Further, we determine several new QECCs and EAQECCs. This paper claims that our obtained codes have improved parameters (e.g. higher minimum distance or greater dimension) than the existing quantum codes. Moreover, we present some detailed examples that effectively illustrate our findings.