Balanced Symmetric Functions over GF(p)

Abstract

Under mild conditions on n, p, we give a lower bound on the number of n-variable balanced symmetric polynomials over finite fields GF(p), where p is a prime number. The existence of nonlinear balanced symmetric polynomials is an immediate corollary of this bound. Furthermore, we prove that X(2t, 2t+1 l-1) are balanced and conjecture that these are the only balanced symmetric polynomials over GF(2).

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2008
Accession Number
ADA574170

Entities

People

  • Pantelimon Stanica
  • Thomas W. Cusick
  • Yuan Li

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Binomials
  • Coefficients
  • Equations
  • Information Operations
  • Information Theory
  • Mathematics
  • Notation
  • Numbers
  • Permutations
  • Polynomials
  • Prime Numbers
  • Probability
  • Sequences
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Graph Algorithms and Convex Optimization.
  • Linear Algebra