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Weierstrass Pure Gaps on Curves With Three Distinguished Points.
- Source :
- IEEE Transactions on Information Theory; May2022, Vol. 68 Issue 5, p3062-3069, 8p
- Publication Year :
- 2022
-
Abstract
- Let $ \mathbb K$ be an algebraically closed field. In this paper, we consider the class of smooth plane curves of degree $n+1>3$ over $ \mathbb K$ , containing three points, $P_{1},P_{2}$ , and $P_{3}$ , such that $nP_{1}+P_{2}$ , $nP_{2}+P_{3}$ , and $nP_{3}+P_{1}$ are divisors cut out by three distinct lines. For such curves, we determine the dimension of certain special divisors supported on $\{P_{1},P_{2},P_{3}\}$ , as well as an explicit description of all pure gaps at each nonempty subset of the distinguished points $P_{1},P_{2}$ , and $P_{3}$. When $ \mathbb K=\overline { \mathbb F}_{q}$ , this class of curves, which includes the Hermitian curve, is used to construct algebraic geometry codes having minimum distance better than the Goppa bound. [ABSTRACT FROM AUTHOR]
- Subjects :
- ALGEBRAIC codes
ALGEBRAIC geometry
ALGEBRAIC curves
PLANE curves
DIVISOR theory
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 156419256
- Full Text :
- https://doi.org/10.1109/TIT.2021.3140195