A sequence of one-point codes from a tower of function fields

Takehiro Hasegawa; Shoichi Kondo; Hidekazu Kurusu

doi:10.1007/s10623-006-9013-x

A sequence of one-point codes from a tower of function fields

Takehiro Hasegawa^*, Shoichi Kondo, Hidekazu Kurusu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	251-267
Number of pages	17
Journal	Designs, Codes, and Cryptography
Volume	41
Issue number	3
DOIs	https://doi.org/10.1007/s10623-006-9013-x
Publication status	Published - 2006 Dec

Keywords

Feng-Rao bound
Minimum distance
One-point code
Tower of function fields

ASJC Scopus subject areas

Theoretical Computer Science
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s10623-006-9013-x

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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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AU - Hasegawa, Takehiro

AU - Kondo, Shoichi

AU - Kurusu, Hidekazu

PY - 2006/12

Y1 - 2006/12

N2 - 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.

AB - 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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KW - Minimum distance

KW - One-point code

KW - Tower of function fields

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A sequence of one-point codes from a tower of function fields

Abstract

Keywords

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