Extension of the field, generates a primitive space matrix Galois
DOI:
https://doi.org/10.18372/2410-7840.17.9785Keywords:
irreducible and primitive polynomials, basic and conjugated matrix Galois and Fibonacci, spatial matrix, extended Galois fieldAbstract
The paper deals with the formation of extended fields, elements of which are Galois matrix representing the spatial non-degenerate matrix synthesized by forming elements – one-dimensional vectors and irreducible polynomials of degree by the method of successive rows of filling. The essence of the method of successive filling option for two-dimensional matrix is reduced to the placement of elements in the lower row of the matrix in which the following lines (bottom to top) fit shifted by one bit to the left vectors lying in the previous line. In the case where a shift length of the vector is greater than the order of the matrix , this vector provides the residue modulo . Introduced Galois conjugate matrix and unambiguously associated right-hand base and conjugate transpose matrix Fibonacci. Discussed the possibility of building advanced fields on the basis of spatial matrices formed by two-dimensional matrix Galois.References
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