Abstract
We construct a series of algebraic geometric codes using a class of curves which have many rational points. We obtain codes of lengthq 2 over\(\mathbb{F}\) q , whereq = 2q 20 andq 0 = 2n, such that dimension + minimal distance ≧q 2 + 1 − q 0 (q − 1). The codes are ideals in the group algebra\(\mathbb{F}\) q [S], whereS is a Sylow-2-subgroup of orderq 2 of the Suzuki-group of orderq 2 (q 2 + 1)(q − 1). The curves used for construction have in relation to their genera the maximal number of\(\mathbb{F}\) GF q -rational points. This maximal number is determined by the explicit formulas of Weil and is effectively smaller than the Hasse—Weil bound.
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Supported by Deutsche Forschungsgemeinschaft while visiting Essen University
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Hansen, J.P., Stichtenoth, H. Group codes on certain algebraic curves with many rational points. AAECC 1, 67–77 (1990). https://doi.org/10.1007/BF01810849
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DOI: https://doi.org/10.1007/BF01810849