Accession Number : AD0640686

Title :   SOME REMARKS ON THE VECTOR SUBSPACES OF A FINITE FIELD,

Corporate Author : HAWAII UNIV HONOLULU DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Pele,R. L.

Report Date : 20 JUN 1966

Pagination or Media Count : 13

Abstract : Let F be a finite field of elements and E an extension of F of degree n. Consider E as a vector space over F. It is shown that for every subspace V of E there exists a unique polynomial whose roots are the elements of V, and there exists a unique polynomial g(X) of the same form, but of degree q(n-r), such that g(E) = V, where r is the dimension of V. Furthermore f(X) and g(X) split completely in E, and f(g(X)) = g(f(X)) = Xq(n) - X. (Author)

Descriptors :   (*CODING, THEORY), ALGEBRA, POLYNOMIALS, TRANSFORMATIONS(MATHEMATICS), VECTOR ANALYSIS

Subject Categories : Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE