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Solving sparse linear equations over finite fields
Abstract
A "coordinate recurrence" method for solving sparse systems of linear equations over finite fields is described. The algorithms discussed all requireO(n_{1}(\omega + n_{1})\log^{k}n_{1})field operations, wheren_{1}is the maximum dimension of the coefficient matrix,\omegais approximately the number of field operations required to apply the matrix to a test vector, and the value ofkdepends on the algorithm. A probabilistic algorithm is shown to exist for finding the determinant of a square matrix. Also, probabilistic algorithms are shown to exist for finding the minimum polynomial and rank with some arbitrarily small possibility of error.
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Cited by
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Metadata
- Authors
- Wiedemann, D.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1986-01
- Volume
- 32
- Issue
- 1
- Pages
- 54-62
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2071483197
- Cited by
- 546
- References
- 0
- FWCI
- 7.63
- Type
- journal article
- Language
- en
- Open access
- closed
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