Codes, Packings and the Critical Problem.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1971
- Accession Number
- AD0722080
Entities
People
- Thomas A. Dowling
Organizations
- University of North Carolina at Chapel Hill