The Minimal Generator Matrix of a Vector Space |
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| Authors: | Morteza Esmaeili T Aaron Gulliver Norman P Secord |
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| Affiliation: | (1) Department of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6 , CA;(2) Department of Systems and Computer Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6, CA;(3) Communications Research Centre, 3701 Carling Avenue, Box 11490, Station H, Ottawa, ON, Canada K2H 8S2, CA |
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| Abstract: | The atomic vectors of a finitely generated vector space C over a field F are characterized for C a subspace of the product vector space ? = ∏
i
=1
n
?
i
over F. For finite fields, the minimal trellis diagram for mixed-codes is determined, and this provides the L-section minimal trellis diagram for linear codes. As an example, an extremely simple yet comprehensive analysis of the trellis
structure of Reed-Muller codes is given. In particular, a trellis oriented generator matrix for the 2
l
-section minimal trellis diagram of a Reed-Muller code is presented.
Received: February 27, 1997; revised version: May 6, 1999 |
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| Keywords: | : Trellis oriented generator matrix Linear block codes Atomic vectors |
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