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Subcovers and Codes on a Class of Trace-Defining Curves.
- Source :
-
IEEE Transactions on Information Theory . Apr2019, Vol. 65 Issue 4, p2101-2106. 6p. - Publication Year :
- 2019
-
Abstract
- In this paper, we construct some class of explicit subcovers of the curve $\mathcal {X}_{n,r}$ defined over $\mathbb {F}_{q^{n}}$ by affine equation $y^{q^{n-1}}+\cdots +y^{q}+y=x^{q^{n-r}+1}-x^{q^{n}+q^{n-r}}$. These subcovers are defined over $\mathbb {F}_{q^{n}}$ by affine equation $g_{s}(y)=x^{q^{n}+q^{n-r}}-x^{q^{n-r}+1}$ , where $g_{s}(y)$ is a $q$ -polynomial of degree $q^{s}$. The Weierstrass semigroup $H(P_\infty)$ , where $P_\infty $ is the only point at infinity on such subcovers, is determined for $1 \leq s \leq 2r-n+1$ , and the corresponding one-point AG codes are investigated. Codes establishing new records on the parameters with respect to the previously known ones are discovered, and 108 improvements on MinT tables are obtained. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 135443207
- Full Text :
- https://doi.org/10.1109/TIT.2018.2868822