Abstract
We construct a sequence of one-point codes from a tower of function fields whose relative minimum distances have a positive limit. Our tower is characterized by principal divisors. We determine completely the minimum distance of the codes from the first field of our tower. These results extend those of Stichtenoth [IEEE Trans Inform Theory (1988), 34(15):1345–1348], Yang and Kumar [Lecture Notes in Mathematics, 1518, (1991), Springer-Verlag, Berlin Hidelberg New York, pp. 99–107], and Garcia [Comm. Algebra, 20(12): 3683–3689]. As an application, we show that the minimum distance corresponds to the Feng–Rao bound.
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Communicated by A. Enge.
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Hasegawa, T., Kondo, S. & Kurusu, H. A sequence of one-point codes from a tower of function fields. Des Codes Crypt 41, 251–267 (2006). https://doi.org/10.1007/s10623-006-9013-x
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DOI: https://doi.org/10.1007/s10623-006-9013-x