Solving sparse linear systems of equations over finite fields using bit-flipping algorithm |
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Authors: | Asieh A. Mofrad M.-R. Sadeghi D. Panario |
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Affiliation: | 1. Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran;2. School of Mathematics and Statistics, Carleton University, K1S 5B6, Ontario, Canada |
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Abstract: | Let Fq be the finite field with q elements. We give an algorithm for solving sparse linear systems of equations over Fq when the coefficient matrix of the system has a specific structure, here called relatively connected. This algorithm is based on a well-known decoding algorithm for low-density parity-check codes called bit-flipping algorithm. We modify and extend this hard decision decoding algorithm. The complexity of this algorithm is linear in terms of the number of columns n and the number of nonzero coefficients ω of the matrix per iteration. The maximum number of iterations is bounded above by m, the number of equations. |
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Keywords: | Bit-flipping Sparse linear systems Finite fields |
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