Two families of BCH codes and construction of quantum codes

Let q ≥ 3 be odd prime power. Maximal designed distances of non-primitive Hermitian dual containing q² - ary BCH codes of length n = (q⁴ -1)/2 and 2(q² -1) are determined. For each given n, a group of non-narrow-sense Hermitian dual containing BCH codes are constructed and their dimensions are computed. Using these non-narrow-sense BCH codes, many new quantum codes are constructed. Our maximal designed distances improve upon the known results in the literature and many of new quantum BCH codes are better than those constructed from narrow-sense BCH codes.