Lumbard, Kim E. and McEliece, Robert J. (1994) Counting minimal generator matrices. In: Proceedings 1994 IEEE International Symposium on Information Theory. IEEE , Piscataway, NJ, p. 18. ISBN 0-7803-2015-8. https://resolver.caltech.edu/CaltechAUTHORS:20120222-134457817
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Abstract
Given a particular convolutional code C, we wish to find all minimal generator matrices G(D) which represent that code. A standard form S(D) for a minimal matrix is defined, and then all standard forms for the code C are counted (this is equivalent to counting special pre-multiplication matrices P(D)). It is shown that all the minimal generator matrices G(D) are contained within the 'ordered row permutations' of these standard forms, and that all these permutations are distinct. Finally, the result is used to place a simple upper bound on the possible number of convolutional codes.
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| Additional Information: | © 1994 IEEE. Date of Current Version: 06 August 2002. McEliece’s contribution was supported in part by AFOSR Grant F49620-94-1-005 and in part by a grant from Pacific Bell. | |||||||||
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| Record Number: | CaltechAUTHORS:20120222-134457817 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120222-134457817 | |||||||||
| Official Citation: | Lumbard, K.E.; McEliece, R.J.; , "Counting minimal generator matrices," Information Theory, 1994. Proceedings., 1994 IEEE International Symposium on , vol., no., pp.18, 27 Jun-1 Jul 1994 doi: 10.1109/ISIT.1994.394953 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=394953&isnumber=8959 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 29418 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 23 Feb 2012 23:32 | |||||||||
| Last Modified: | 03 Oct 2019 03:41 |
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