SOME CODES WHICH ARE INVARIENT UNDER A DOUBLY-TRANSITIVE PERMUTATION GROUP AND THEIR CONNECTION WITH BALANCED INCOMPLETE BLOCK DESIGNS

Abstract

If a binary code is invariant under a doubly-transitive permutation group, then the set of all code words of weight j forms a balanced incomplete block design. Besides the extended normal BCH codes and the extended quadratic residue codes, the Reed-Muller codes are proven to be invariant under a doubly- transitive permutation group. Thus, BIB designs can be derived from these classes of codes. It is shown that if the symbols of the Reed-Muller codes are properly arranged, and if the first digit is omitted, then all Reed-Muller codes are cyclic.

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Document Details

Document Type
Technical Report
Publication Date
Jan 28, 1966
Accession Number
AD0631865

Entities

People

  • Shu Lin
  • Tadao Kasami

Organizations

  • University of HawaiĘ»i System

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Air Force
  • Bits
  • Coding
  • Contracts
  • Decoding
  • Electrical Engineering
  • Engineering
  • Experimental Design
  • Generators
  • Mathematics
  • Permutations
  • Polynomials
  • Symbols
  • United States
  • Universities
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

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