EUCLIDEAN GEOMETRY CYCLIC CODES,

Abstract

A class of Random-error-correcting cyclic codes is defined and investigated. It is shown that a suitable choice of generator polynomial guarantees that the polynomials corresponding to all subspaces of a given dimensionality in a particular Euclidean geometry are in the null space of the code. These subspaces (flats) are useful in deriving a seemingly tight lower bound on the minimum distance of the codes. This bound shows that for practical values of code length the codes are rather efficient random-error-correctors, although not quite as efficient as the Bose-Chaudhuri-Hocquenghem codes. The class of Euclidean geometry codes, as they have been called, contains the class of Reed-Muller codes. It is shown that with a slight modification the decoding algorithm for these latter codes can be applied to the Euclidean geometry codes. This algorithm, referred to in the literature both as the Reed Algorithm and majority-logic decoding, can be implemented in a surprisingly simple manner. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 15, 1967
Accession Number
AD0654675

Entities

People

  • E. J. Weldon Jr

Organizations

  • University of HawaiĘ»i System

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Coding
  • Decoding
  • Generators
  • Geometry
  • Guarantees
  • Literature
  • Mathematics
  • Notation
  • Polynomials

Readers

  • Computer Programming and Software Development.
  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.

Technology Areas

  • Space