Search results for "Galois ring"

showing 2 items of 2 documents

A-Codes from Rational Functions over Galois Rings

2006

In this paper, we describe authentication codes via (generalized) Gray images of suitable codes over Galois rings. Exponential sums over these rings help determine--or bound--the parameters of such codes.

Discrete mathematicsMathematics::Commutative AlgebraApplied MathematicsFundamental theorem of Galois theoryGalois groupRational functionExponential polynomialComputer Science ApplicationsEmbedding problemDifferential Galois theorysymbols.namesakeGalois rings Gray map codesComputer Science::Computer Vision and Pattern RecognitionComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComputer Science::MultimediasymbolsSettore MAT/03 - GeometriaGalois extensionResolventMathematicsDesigns, Codes and Cryptography
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Finite Commutative Rings and Their Applications

2002

Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

Settore MAT/02 - AlgebraCommutative finite ringsGalois ring finite commutative ringCodes and CriptographyCommutative finite rings Codes and Criptography
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