ON THE WEIGHT STRUCTURE AND SYMMETRY OF BCH CODES.

Abstract

Weight distributions found by digital computation are given for a number of Bose-Chaudhuri-Hocquenghem codes of length (2 to m power)-1 for m as large as ten. The minimum weight was determined in some additional cases which include all non-trivial double, triple, and quadruple error correcting codes by theoretical results and by computer search. In each known case, the true minimum weight meets the Bose-Chaudhuri-Hocquenghem lower bound. It was observed that ja subj = (n + 1 - j)a sub (n + 1 - j) for all BCH codes for which weights were computed, where n is the code length and a sub j the number of code words of weight j. It is shown that a BCH code extended by the addition of an overall parity check is invarient under permutations of the doublytransitive affine group, and the observed equation holds as a consequence of this symmetry. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jul 10, 1965
Accession Number
AD0626730

Entities

People

  • W. Wesley Peterson

Organizations

  • University of HawaiĘ»i System

Tags

DTIC Thesaurus Topics

  • Computations
  • Computers
  • Equations
  • Mathematics
  • Symmetry

Readers

  • Analytical Mechanics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.