A sequence of one-point codes from a tower of function fields |
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| Authors: | Takehiro Hasegawa Shoichi Kondo Hidekazu Kurusu |
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| Affiliation: | (1) Department of Mathematics, School of Education, Waseda University, Tokyo 169-805, Japan;(2) Graduate School of Science and Engineering, Waseda University, Tokyo 169-8555, Japan |
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| 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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| Keywords: | Tower of function fields One-point code Minimum distance Feng– Rao bound |
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