Construction of large-dimensional hulls of BCH codes with length $ n = \frac{q^4-1}{q+1} $
Ming Yan, Tongjiang Yan, Yuhua Sun · Advances in Mathematics of Communications · 2025
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.