AMC
Weierstrass semigroup and codes over the curve $y^q + y = x^{q^r + 1}$
Alonso Sepúlveda Guilherme Tizziotti
Advances in Mathematics of Communications 2014, 8(1): 67-72 doi: 10.3934/amc.2014.8.67
We compute the Weierstrass semigroup at a pair of rational points on the curve defined by the affine equation $y^q + y = x^{q^r + 1}$ over $\mathbb{F}_{q^{2r}}$, where $r$ is a positive odd integer and $q$ is a prime power. We then construct a two-point AG code on the curve whose relative parameters are better than comparable one-point AG code.
keywords: Weierstrass semigroups maximal curves AG codes.
AMC
Castle curves and codes
Carlos Munuera Alonso Sepúlveda Fernando Torres
Advances in Mathematics of Communications 2009, 3(4): 399-408 doi: 10.3934/amc.2009.3.399
We introduce two types of curves of interest for coding theory purposes: the so-called Castle and weak Castle curves. We study the main properties of codes arising from these curves.
keywords: algebraic curves. Linear codes Weierstrass semigroups one-point algebraic geometry codes

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