23 February 1988 A Theoretical Foundation For The Weighted Checksum Scheme
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The weighted checksum scheme has been proposed as a low-cost error detection procedure for parallel matrix computations. Error correction has proved to be a much more difficult problem to solve than detection when using weighted checksums. In this paper we provide a theoretical basis for the correction problem. We show that for a distance d+1 weighted checksum scheme, if a maximum of ici [d/2] errors ensue then we can determine exactly how many errors have occurred. We further show that in this case we can correct the errors and give a procedure for doing so.
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Cynthia J. Anfinson, Cynthia J. Anfinson, Richard P. Brent, Richard P. Brent, Franklin T. Luk, Franklin T. Luk, } "A Theoretical Foundation For The Weighted Checksum Scheme", Proc. SPIE 0975, Advanced Algorithms and Architectures for Signal Processing III, (23 February 1988); doi: 10.1117/12.948486; https://doi.org/10.1117/12.948486

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