SOME REMARKS ON THE VECTOR SUBSPACES OF A FINITE FIELD,

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)

Document Details

Document Type
Technical Report
Publication Date
Jun 20, 1966
Accession Number
AD0640686

Entities

People

  • R. L. Pele

Organizations

  • University of HawaiĘ»i System

Tags

DTIC Thesaurus Topics

  • Mathematics
  • Polynomials
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Linear Algebra
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space