A maximum distance separable (MDS) block code is a linear code whose distance is maximal among all linear block codes of ratek/n. It is well known that MDS block codes do exist if the field size is more thann. In this paper we generalize this concept to the class of convolutional codes of a fixed ratek/n and a fixed code degree δ. In order to achieve this result we will introduce a natural upper bound for the free distance generalizing the Singleton bound. The main result of the paper shows that this upper bound can be achieved in all cases if one allows sufficiently many field elements.

Authors and Affiliations

1. Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA (e-mail: Rosenthal.1@nd.edu; Smarandache.1@nd.edu), , , , , , US

   Joachim Rosenthal & Roxana Smarandache

Received: December 10, 1998; revised version: May 14, 1999

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