  The syndrome decoding problem has been proposed as a computational hardness
assumption for code based cryptosystem that are safe against quantum computing.
The problem has been reduced to finding the codeword with the smallest non-zero
columns that would satisfy a linear check equation. Variants of Information set
decoding algorithms has been developed as cryptanalytic tools to solve the
problem. In this paper, we study and generalize the solution to codes
associated with the totally non-negative Grassmannian in the Grassmann metric.
This is achieved by reducing it to an instance of finding a subset of the
plucker coordinates with the smallest number of columns. Subsequently, the
theory of the totally non negative Grassmann is extended to connect the concept
of boundary measurement map to Tanner graph like code construction while
deriving new analytical bounds on its parameters. The derived bounds shows that
the complexity scales up on the size of the plucker coordinates. Finally,
experimental results on decoding failure probability and complexity based on
row operations are presented and compared to Low Density parity check codes in
the Hamming metric.
