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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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