A Weight Formula for Group Codes

Abstract

For n odd, let A be any (k,n) group code, i.e. a k-dimensional subset of the vector space of dimension n over the field F of two elements. The eight of a vector is defined to be the number of components in a vector equal to unity. The exponential weight of a vector which is an element of a finite field over F is introduced. Using the general representation of group codes in Solomon (LLGR 47G-0020), a formula is obtained for the exponential weight of a vector as a function of several independent variables, the parameters of the general representation. The coefficients of the formula are obtained using elementary multiplication on the cyclic group of the nth roots of unity.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 09, 1961
Accession Number
AD0264999

Entities

People

  • Gustave Solomon

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Computations
  • Computer Programming
  • Computers
  • Corporations
  • Generators
  • Government Procurement
  • Governments
  • Inventions
  • Mathematical Analysis
  • Mathematics
  • Polynomials
  • Procurement
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computer Programming and Software Development.
  • Statistical inference.

Technology Areas

  • Space
  • Space - Hall-Effect Thruster