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Maximum distance separable convolutional codes


Rosenthal, J; Smarandache, R (1999). Maximum distance separable convolutional codes. Applicable Algebra in Engineering, Communication and Computing, 10(1):15-32.

Abstract

A maximum distance separable (MDS) block code is a linear code whose distance is maximal among all linear block codes of rate k/n. It is well known that MDS block codes do exist if the field size is more than n. In this paper we generalize this concept to the class of convolutional codes of a fixed rate k/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.

Abstract

A maximum distance separable (MDS) block code is a linear code whose distance is maximal among all linear block codes of rate k/n. It is well known that MDS block codes do exist if the field size is more than n. In this paper we generalize this concept to the class of convolutional codes of a fixed rate k/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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Convolutional codes, MDS block codes
Language:English
Date:1999
Deposited On:12 Mar 2010 08:18
Last Modified:06 Dec 2017 20:56
Publisher:Springer
ISSN:0938-1279
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s002000050120
Related URLs:http://www.nd.edu/~rosen/Paper/mds.ps

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