Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces - Aubry, Yves; Berardini, Elena; Herbaut, Fabien; Perret, Marc (Arithmetic, Geometry, Cryptography and Coding Theory)
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