A NEW CLASS OF CODES

Abstract

Error correcting codes of all (k,p) group codes (p-odd), i.e. linear mappings of k-tuples of zeros and ones into p-tuples of zeros and ones, are viewed as a purely algebraic problem. This problem concerns the zeros of certain polynomials on pth roots of unity. These polynomials are parametrized via elements of subgroups of the smallest field containing the pth roots of unity. The so-called jump-shift register codes are also treated. These are ((p + 1)/2, p) single error-correcting codes for p a prime for which 2 has multiplicative order p-1. These noncyclic codes are placed in a pseudo-cyclic setting and are easily encodable and decodable. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 28, 1961
Accession Number
AD0255696

Entities

People

  • Gustave Solomon

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Circuits
  • Electrical Circuits
  • Electrical Equipment
  • Electronic Circuits
  • Electronic Equipment
  • Flip Flop Circuits
  • Logic Devices
  • Logic Gates
  • Mathematics
  • Polynomials
  • Shift Registers

Fields of Study

  • Mathematics

Readers

  • Computer Programming and Software Development.
  • Graph Algorithms and Convex Optimization.
  • Linear Algebra