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<p>A generalization of existing real numer codes is proposed. It is proven that linearity is a necessary and sufficient condition for codes used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU decomposition. It is also proven that for every linear code defined over a finite field, there exists a corresponding linear real-number code with similar error detecting capabilities. Encoding schemes are given for some of the example codes which fall under the general set of real-number codes. With the help of experiments, a rule is derived for the selection of a particular code for a given application. The performance overhead of fault tolerance schemes using the generalized encoding schemes is shown to be very low, and this is substantiated through simulation experiments.</p>
real number codes; encoding; fault-tolerant matrix operations; processor arrays; linearity; necessary and sufficient condition; multiplication; transposition; LU decomposition; error detecting; performance overhead; simulation experiments; encoding; error detection codes; fault tolerant computing.

V. Nair and J. Abraham, "Real-Number Codes for Fault-Tolerant Matrix Operations on Processor Arrays," in IEEE Transactions on Computers, vol. 39, no. , pp. 426-435, 1990.
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