Construction of Larger Dimensional Hulls of BCH Codes with Length n=q⁴-1/q+1

Abstract Hulls of linear codes are widely applied in constructing self-orthogonal codes and quantum codes, as well as in various other aspects. Let Fq be the finite field of order q and n=q⁴-1/q+1, where q is an odd prime power. Let C be a BCH code over Fq with length n and dimension k. In this paper, we provide the necessary and sufficient conditions for C possessing a hull with dimension $k-1$ or k⊥-1, where k⊥ is the dimension of the dual code of C, while also deriving several classes of self-orthogonal codes, including some optimal codes.