On additive cyclic codes over $\mathbb{F}_4+u\mathbb{F}_4$

Source abstract

This article studies additive cyclic codes over $R = \mathbb{F}_4+u\mathbb{F}_4$, 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 $\mathbb{F}_4$ 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 $\mathbb{F}_4$. 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.Accepted: 20 February 2025