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Conversion of Element Representations in Galois Rings


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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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).

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  • Galois rings
  • Teichmüller elements
  • Symbolic computation

Mathematics Subject Classification

  • 13B05
  • 13F20
  • 12K99