Enumeration of stopping sets of full-rank parity-check matrices of hammng codes

Abstract

Iterative techniques have been proposed for decoding linear binary block codes over erasure channels. The performance of such decoding techniques depends on the parity-check matrices used, and in partivular, on the numbers and sizes of stopping sets of these matrices. In the 2004 Shannon lecture, McElliece presented an expression for the number of stopping sets of size three for a full-rank parity-check matrix of the Hamming code. In this paper, we present an expression for the number of stopping sets of any given size for the same parity-check matrix.