On a Class of Codes of Delsarte

Abstract

In reference [1], Delsarte generalized a class of codes due to Chien and Choy [2] which, in turn, are a generalization of Goppa Codes [3]. Delsarte shows that almost all of these codes meet the Gilbert-Varsharmov bound, a result which is also true of Goppa codes [4]. Both of these results are obtained by showing that the actual minimum distance is much larger than the "designed" distance and approaches the G-V bound for the designed rate. This talk raises the question as to how large the actual rate can be for fixed design distance. No new theorems are presented but two well known theorems are proved in the context of Delsarte's presentation.