On additive cyclic codes over F_4+uF_4

Abstract

This article studies additive cyclic codes over R = F4 + uF4, where u^2 = 0. We obtain generator polynomials for these codes and provide necessary
and sufficient conditions for additive codes to be self-orthogonal and self-dual codes over R with respect to the symplectic inner product. Additive self-orthogonal codes over F4 with respect to the symplectic inner product are used to construct quantum codes. We demonstrate that the Gray image of additive self-orthogonal codes over R results in additive self-orthogonal codes over F4. Additionally, we prove that binary self-orthogonal codes can be obtained from additive self-orthogonal codes over R with respect to the symplectic inner product.