Abstract
In this paper, we investigate all coset leaders of primitive BCH codes for $$\delta$$ in the range $$1\le \delta \le q^\frac{m+7}{2}$$ , which extends Liu and Shi’s results. Besides, we also generalize Shi’s results by proposing the maximum designed distance of non-narrow-sense( $$b=k_2q^2+k_1q+k_0$$ ) primitive BCH codes which can contain their Euclidean dual. At the end, we calculate the dimension of the Euclidean dual containing non-narrow-sense primitive BCH codes and construct some quantum BCH codes.
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