New AI Algorithm Based On Galois Field through Kronecker Product for Digital Transaction
Keywords:
AI, Finite field, Finite ring, Galois group, Hypesurface, Linear transformation, MatrixAbstract
This paper presents the application of Galois Group. This is a non-binary AI algorithm over the finite field. This paper reviewed this algorithm in context to generate the optimal syndrome and optimal error locator polynomial by the matrix equation defined by the trace. Next application deals with the study of equations over the finite fields under the hypersurfaces characteristics. There are new results on affine hypersurfaces over the n-dimensional affine space defined by the equation This is transformed into matrix equation to count its rational point efficiently with the propsed algorithm based on discrete algebraic varieties defined by the matrix by an algebraic closure characteristics. The new approach on estimation under the finite field is studied by Hal’asz on the foundation of Estimates for the concentration function of combinatorial number theory and probability later this is transformed into a beautiful work on random matrix through the question as “How random is the characteristic polynomial of a random matrix? This dealt on the solving the linear equations based on counting the points over the finite field. They studied the limiting behavior of the number of solutions of a system of random linear equations over a finite field and a finite ring. For AI applications, there are several new methods are submitted to solve the equation over the finite field. Another noteworthy literature on this result is the cycle structure of a linear transformation over a finite field.
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