Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces
Yves Aubry, Elena Berardini, Fabien Herbaut, Marc Perret · Contemporary mathematics - American Mathematical Society · 2021
We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds for surfaces whose arithmetic Picard number equals one, surfaces without curves with small self-intersection and fibered surfaces. Finally we specify our bounds to the case of surfaces of degree $d\geq 3$ embedded in $\mathbb{P}^3$.