A Decomposition Theory for Binary Linear Codes

The decomposition theory of matroids initiated by Paul Seymour in the 1980's has had an enormous impact on research in matroid theory. This theory, when applied to matrices over the binary field, yields a powerful decomposition theory for binary linear codes. In this paper, we give an overview of this code decomposition theory, and discuss some of its implications in the context of the recently discovered formulation of maximum-likelihood (ML) decoding of a binary linear code over a binary-input discrete memoryless channel as a linear programming problem. We translate matroid-theoretic results of Gr

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Navin Kashyap
• Keywords: Binary Linear Code, CORR 2006, Decomposition Theory, Education, Powerful Decomposition Theory