## A theory of algorithm-based fault tolerance |

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### Contents

The Detection Problem | 10 |

Error Correction and the Correction Problem | 19 |

Practical Weight Selection for Multiple Error Detection | 26 |

Copyright | |

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### Common terms and phrases

Abraham 12 algorithm Algorithm-based fault tolerance Anfinson checksum method choose code space defined coding scheme coding theory coefficients column checksum matrix columns is linearly columns of H Corollary correction procedure correction vector d x d identity matrix Definition Denote detect d errors dist(y distance domain of H eigenvalues elementary row operations encoded error protection errors occur fault model finite field H are linearly Hence Huang and Abraham Jou and Abraham least d+1 linearly dependent columns linearly independent matrix B mod minimum weight modular arithmetic multiple error detection nonsingular nonzero elements null space number of errors parity check matrix Proof prove QR decomposition rank(K Reed-Solomon code row checksum matrix satisfies the condition set of weights signal processing singular value decomposition soft error syndrome vector systolic arrays Theorem 3.3 unique Vandermonde matrix vectors in N(H weight d+1 weight vectors weighted checksum matrix weighted checksum scheme weighted column checksum word length