Subcovers and Codes on a Class of Trace-Defining Curves

Author(s)

Borges Filho, Herivelto Martins ^[1] ; Castellanos, Alonso Sepulveda ^[2] ; Tizziotti, Guilherme Chaud ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13566590 Sao Paulo - Brazil

^[2] Univ Fed Uberlandia, Fac Matemat, BR-38408100 Uberlandia, MG - Brazil

• Document type: Journal article
• Source: IEEE TRANSACTIONS ON INFORMATION THEORY; v. 65, n. 4, p. 2101-2106, APR 2019.
• Web of Science Citations: 0

Abstract

In this paper, we construct some class of explicit subcovers of the curve X-n,X- r defined over F-q(n) by affine equation y(qn-1) + center dot center dot center dot + y(q) + y = x(qn-r)+(1)-x(qn)+ q(n-r). These subcovers are defined over Fqn by affine equation g(s)(y) = x(qn)+ q(n-r) -xq(n-r)+(1), where g(s)(y) is a q-polynomial of degree q(s). The Weierstrass semigroup H(P-infinity), where P-infinity is the only point at infinity on such subcovers, is determined for 1 <= s <= 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. (AU)

• FAPESP's process: 17/04681-3 - Algebraic curves over finite fields
• Grantee: Herivelto Martins Borges Filho
• Support Opportunities: Regular Research Grants