Ensemble Analysis on Syndrome Entropy of Binary Linear Codes

Syndrome entropy of a binary linear code is the entropy corresponding to a product of a binary m times n matrix and a vector of length n generated from a binary i.i.d. source. In this paper, we investigate the syndrome entropy of a matrix contained in an ensemble of m times n binary matrices such as constant row weight ensembles. In the analysis, the first and the second moment of the coset weight distribution of an ensemble play a crucial role