
Accession Number : AD0722080
Title : Codes, Packings and the Critical Problem.
Descriptive Note : Rept. for Feb 69Jun 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 wellknown 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