STEP-BY-STEP DECODING IN GROUPS WITH A WEIGHT FUNCTION. PART 1

Abstract

Let G be a group with a weight (norm) w, and thus a distance. Let H be a normal subgroup of G. A basic lemma connects w-decomposition in G with that in the factor group G/H. One application is the justification of a general, operationally useful, concept of step-by-step decoding of G into H. A second application is to the study of a question of Slepian's: When can a set of unique coset representatives one element of minimal weight from each H- coset, be chosen so that this set of representatives is closed under descendance. A sufficient condition, independent of H, is proved. In particular, the answer is positive for groups G with Hamming or Lee weight functions.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1961
Accession Number
AD0268032

Entities

People

  • Eugene Prange

Organizations

  • Air Force Cambridge Research Laboratories

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Air Force
  • Concrete
  • Construction
  • Decoding
  • Decomposition
  • Generators
  • Government Procurement
  • Governments
  • Identities
  • Numbers
  • Real Numbers
  • Triangles
  • United States
  • Verification

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Systems Analysis and Design