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In this paper, we present an analog of the Singleton bound for convolutional codes over finite rings. Codes meeting that bound are called MDS. A constructive method for the MDS codes, restricted to free codes, is presented via cyclic codes over finite rings. Examples of nonfree MDS codes are provided.
Our aim is to study codes overZpr satisfying two distinct Singleton type bounds. We describe the smallest free code containing an MDR code and give explicit expressions for the submodules quotients defined in Norton and Sǎlǎgean (2000b).
An important class of codes widely used in applications is the class of convolutional codes. Most of the literature of convolutional codes is devoted to convolutional codes over finite fields. The extension of the concept of convolutional codes from finite fields to finite rings have attracted much attention in recent years due to fact that they are the… (More)