On the minimum distance of Castle codes

Castle codes are algebraic geometry one-point codes on Castle curves. This family contains some of the most important AG codes among those studied in the literature to date. The minimum distance of these codes can be bounded by using the order-like bound d⁎, which is known to be equivalent to the classical order bound when both can be applied. In this paper we compute d⁎ for some Castle codes, including those related to semigroups generated by two elements and telescopic semigroups. In particular we compute the bound d⁎ in full for Suzuki codes.