On the Construction of 1-D 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 behavior 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 are explicitly computed for families of 1-D convolutional Goppa codes.