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On Minimal Realization Over a Finite Chain Ring

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Abstract

Let R be a finite chain ring, e.g. a Galois ring. We give a compact recursive formula for a minimal realization of a finite R-sequence. In particular, we show how to obtain a monic minimal polynomial and a rational approximation of a finite R-sequence. We also show how to solve the classical key equation of Algebraic Coding Theory over R.

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Authors and Affiliations

  1. Algebraic Coding Research Group, Centre for Communications Research, University of Bristol, England

    Graham Norton

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  1. Graham Norton
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Norton, G. On Minimal Realization Over a Finite Chain Ring. Designs, Codes and Cryptography 16, 161–178 (1999). https://doi.org/10.1023/A:1008341129955

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