Year: 2025
Type: article
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
Institutions: Indian Institute of Technology Delhi, South Asian University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413932984