Construction of Larger Dimensional Hulls of BCH Codes with Length $n=\frac{q^4-1}{q+1}$
Ming Yan, Tongjiang Yan, Yuhua Sun · Research Square · 2024
Abstract Hulls of linear codes are widely applied in constructing self-orthogonal codes and quantum codes, as well as in various other aspects. Let $\mathbb{F}_q$ be the finite field of order $q$ and $n=\frac{q^4-1}{q+1}$, where $q$ is an odd prime power. Let $\mathcal{C}$ be a BCH code over $\mathbb{F}_q$ with length $n$ and dimension $k$. In this paper, we provide the necessary and sufficient conditions for $\mathcal{C}$ possessing a hull with dimension $k-1$ or $k^{\perp}-1$, where $k^{\perp}$ is the dimension of the dual code of $\mathcal{C}$, while also deriving several classes of self-orthogonal codes, including some optimal codes.