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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.