On the construction of 1-dimensional MDS convolutional Goppa codes

Abstract

We show that the free distance, as a function on a space parameterizing a family of convolutional codes, is a lower-semicontinuous function and that, therefore, the property of being Maximum Distance Separable (MDS) is an open condition. For a class of convolutional codes, an algorithm is offered to compute the free distance. The behaviour of the free distance by enlargements of the alphabet and by increasing the length is also studied. As an application, the algebraic equations characterizing the subfamily of MDS codes is explicitly computed for families of 1-dimensional convolutional Goppa codes (CGC).