Subcovers and Codes on a Class of Trace-Defining Curves

In this paper, we construct some class of explicit subcovers of the curve X
_n,r
defined over F
_q(n)
by affine equation y
^q(n-1)
+ ··· + y
^q
+ y = x
^q(n-r)+1
- x
^q(n)+q(n-r)
. These subcovers are defined over 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
_∞
), where P
_∞
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.