Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
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A memory efficient form of solving linear systems modulo 2
ResourceFunction["BitStringLinearSolve"][{n_{1},n_{2},…},rhs,ncols]] solves the linear system {n_{1},n_{2},…}.x=rhs where {n_{1},n_{2},…} is a list of integers corresponding to bit vectors of length ncols, and rhs is an explicit vector of zeros and ones. 
Solve a simple example for a bit vector:
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Create a random matrix of bit vectors and a random right hand side:
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Solve the corresponding linear system modulo 2:
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Create a large array of bit strings to use as a matrix, along with a suitable right hand side vector:
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ResourceFunction["BitStringLinearSolve"] is especially useful when working with matrices that might otherwise require excessive memory:
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Here is the matrix from which the bit vectors were created:
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We see that the prior result agrees with LinearSolve:
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Similarly, create a matrix of explicit 0‐1 vectors corresponding to the large integers:
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LinearSolve is substantially slower as compared to ResourceFunction["BitStringLinearSolve"]:
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Check that the results are the same:
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Wolfram Language 11.3 (March 2018) or above
This work is licensed under a Creative Commons Attribution 4.0 International License