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Conversion of Element Representations in Galois Rings

Mathematics in Computer Science volume 14, pages 209–222 (2020)Cite this article

Abstract

We are developing a symbolic calculator in order to computationally operate within Galois rings algebraic structure. In any Galois ring, whose characteristic is a power of a prime, each element has an additive representation, which is basically a remainder polynomial when dividing by a basic irreducible polynomial, and a p-adic representation given by Teichmüller elements, which are powers of roots of basic primitive polynomials. In this paper we introduce basic procedures to obtain Hensel’s lifts of primitive polynomials and the conversion between additive and p-adic representations.

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Authors and Affiliations

  1. Computer Science, CINVESTAV-IPN, Mexico City, Mexico

    Juan Carlos Ku-Cauich & Guillermo Morales-Luna

Authors
  1. Juan Carlos Ku-Cauich
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  2. Guillermo Morales-Luna
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Correspondence to Juan Carlos Ku-Cauich.

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Ku-Cauich, J.C., Morales-Luna, G. Conversion of Element Representations in Galois Rings. Math.Comput.Sci. 14, 209–222 (2020). https://doi.org/10.1007/s11786-019-00440-5

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  • DOI: https://doi.org/10.1007/s11786-019-00440-5

Keywords

  • Galois rings
  • Teichmüller elements
  • Symbolic computation

Mathematics Subject Classification

  • 13B05
  • 13F20
  • 12K99