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Vector Form of the Finite Fields GF(pm)*.
Authors: N. A. Moldovyan, P. A. Moldovyanu
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Abstract
Specially defined multiplication operation in the m-dimensional vector space (VS) over a ground finite field (FF) imparts properties of the extension FF to the VS. Conditions of the vector FF (VFF) formation are derived theoretically for cases m=2 and m=3. It has been experimentally demonstrated that under the same conditions VFF are formed for cases m=4, m=5 and m=7. Generalization of these results leads to the following hypotheses: for each dimension value m the VS defined over a ground field GF(p), where p is a prime and m|p-1 , can be transformed into a VFF introducing special type of the vector multiplication operations that are defined using the basis-vector multiplication tables containing structural coefficients. The VFF are formed in the case when the structural coefficients that could not be represented as the m-th power of some elements of the ground field are used. The VFF can be also formed in VS defined over extension FF represented by polynomials. The VFF present interest for cryptographic application.E-mail: ,
Fulltext
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Contents
- Some extensions of the Buhlmann-Straub credibility formulae.
- Postoptimal analysis of multicriteria combinatorial center location problem.
- Flow of an Unsteady Dusty Visco-Elastic Fluid Between Two Moving Plates in Frenet-Frame Field System.
- On preradicals associated to principal functors of module categories. II
- On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups.
- Vector Form of the Finite Fields GF(pm)*.
- A lower bound for a quotient of roots of factorials.
- Some more results on b-Θ -open sets.
- Singular limits of solutions to the Cauchy problem for second order linear differential equations in Hilbert spaces.
- Free Moufang loops and alternative algebras.
- On π-quasigroups isotopic to abelian groups.
- Academician Vladimir Arnautov 70th anniversary.
- Academician Iurie Reabuhin 70th anniversary.
