On a Combinatorial Conjecture

Abstract

Recently, Tu and Deng proposed a combinatorial conjecture about binary strings and, on the assumption that the conjecture is correct, they obtained two classes of Boolean functions that are both algebraic immunity optimal, the first class of which are also bent functions. The second class gives balanced functions, which have optimal algebraic degree and the best nonlinearity known until now. In this paper, using three different approaches, we prove that this conjecture is true in many cases with different counting strategies. We also propose some problems about the weight equations that are related to this conjecture. Because of the scattered distribution, we predict that an exact count will be difficult to obtain, in general.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2011
Accession Number
ADA548764

Entities

People

  • Pantelimon Stanica
  • Thomas W. Cusick
  • Yuan Li

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Classification
  • Equations
  • Information Operations
  • Mathematical Analysis
  • Mathematics
  • Number Theory
  • Numbers
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.