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The Minimal Generator Matrix of a Vector Space

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

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 2l-section minimal trellis diagram of a Reed-Muller code is presented.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6 , , , , , , CA

    Morteza Esmaeili

  2. Department of Systems and Computer Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6, , , , , , CA

    T. Aaron Gulliver

  3. Communications Research Centre, 3701 Carling Avenue, Box 11490, Station H, Ottawa, ON, Canada K2H 8S2, , , , , , CA

    Norman P. Secord

Authors
  1. Morteza Esmaeili
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  2. T. Aaron Gulliver
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  3. Norman P. Secord
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Additional information

Received: February 27, 1997; revised version: May 6, 1999

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Esmaeili, M., Gulliver, T. & Secord, N. The Minimal Generator Matrix of a Vector Space. AAECC 10, 1–14 (1999). https://doi.org/10.1007/s002000050119

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  • DOI: https://doi.org/10.1007/s002000050119