Algebraic Geometry Codes from Castle Curves

One- and Two-Point Codes Over Kummer Extensions

“…Homma, Kim and Matthews [11,14] studied two-point codes and applied their results to the Hermitian curve. 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.…”

An Introduction to Algebraic Geometry Codes

“…In this case the Suzuki curve has genus g = 14 and 65 rational points. A plane model of S is given by the equation Then 46,44,43,42,41,40,39,38,36,35,34,33,32,31,30,29,28,28,26,25,24,23,22,21,20,21,18,19,16,17,16,13,12,14,10,13,8,12,10,9,8,8,6,8,7,4,5,4,4,4,5,4…”

Sobre la distancia mínima de códigos AG unipuntuales castillo

“…Consideremos la secuencia de códigos AG unipuntuales (C m ) m≥1 , donde C m := C(X , D, mQ). Los parámetros de los códigos C m se pueden estudiar de manera unificada independiente de la curva X , ver [14].…”

“…Las curvas que alcanzan la igualdad en dicha cota cumplen con los requisitos exigidos. Estas se conocen como curvas castillo (llamadas así por Munuera et al [14]) y los códigos obtenidos tienen excelentes parámetros y pueden ser estudiados de manera unificada sin importar la curva.…”