| Full text | |
| Author(s): |
Borges Filho, Herivelto Martins
;
Cunha, Gregory Duran
Total Authors: 2
|
| Document type: | Journal article |
| Source: | IEEE TRANSACTIONS ON INFORMATION THEORY; v. 68, n. 5, p. 8-pg., 2022-05-01. |
| Abstract | |
Let K be an algebraically closed field. In this paper, we consider the class of smooth plane curves of degree n + 1 > 3 over 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 K = (F) over bar (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. (AU) | |
| FAPESP's process: | 18/01548-3 - Weierstrass points on curves over finite fields and applications |
| Grantee: | Grégory Duran Cunha |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |