Accession Number:

AD0722080

Title:

Codes, Packings and the Critical Problem.

Descriptive Note:

Rept. for Feb 69-Jun 70,

Corporate Author:

NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s):

Report Date:

1971-02-01

Pagination or Media Count:

23.0

Abstract:

The report discusses a new approach to a central problem of coding theory. For a given block length and minimum distance constraint, the information rate of a linear code over a finite field is maximized when the code subspace has maximum dimension. The problem of determining this maximum dimension, called the coding problem here, can be viewed as a critical problem in combinatorial geometry. As such, its solution depends only on the lattice of subspaces of a certain subgeometry of projective geometry. From knowledge of the characteristic polynomial of this lattice one can immediately determine the maximum dimension of a linear code. The central problem, which is only briefly discussed here, is to determine this polynomial. The well-known connection of the coding problem with the packing problem of projective geometry enables one to approach the packing problem by these methods as well. Author

Subject Categories:

  • Cybernetics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE