Weierstrass semigroup and codes over the curve $y^q + y = x^{q^r + 1}$

On Weierstrass semigroup at m points on curves of the form f(y)=g(x)

“…(2) (y) = P 2 + · · · + P a+1 − aP 1 , For a = 5 and b = 7 we have that Γ(P 1 , P 2 ) = {(23, 1), (18, 2), (13,3), (8,4), (3,5), (16,8), (11,9), (6,10), (1,11), (9,15), (4,16), (2,22)} .…”

One- and Two-Point Codes Over Kummer Extensions

“…In [16] Munuera, Sepúlveda and Torres considered codes over a Castle curve, which is a generalization of the Hermitian curve. Recently, Sepúlveda and Tizziotti [17] studied two-point codes over the F q 2ℓ -maximal curve whose affine plane model is given by y q ℓ +1 = x q + x.…”

AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves

“…AG codes from the Hermitian curve have been widely investigated; see [10,[24][25][26]44,46,47] and the references therein. Other constructions based on the Suzuki curve and the curve with equation y q + y = x q r +1 can be found in [36] and [42]. More recently, AG Codes from the GK curve have been constructed in [2,4,11].…”