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) : Dowling,Thomas A.

Report Date : FEB 1971

Pagination or Media Count : 23

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)

Descriptors :   (*CODING, PROJECTIVE GEOMETRY), SET THEORY, SEQUENCES(MATHEMATICS), MATRICES(MATHEMATICS), VECTOR SPACES, POLYNOMIALS, COMBINATORIAL ANALYSIS

Subject Categories : Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE