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<p>We present a linear algebraic formulation for a class of index transformations such asGray code encoding and decoding, matrix transpose, bit reversal, vector reversal,shuffles, and other index or dimension permutations. This formulation unifies, simplifies,and can be used to derive algorithms for hypercube multiprocessors. We show how all the widely known properties of Gray codes, and some not so well-known properties as well, can be derived using this framework. Using this framework, we relate hypercube communications algorithms to Gauss-Jordan elimination on a matrix of 0's and 1's.</p>
Index Termslinear algebra; encoding; decoding; Gray codes; hypercube networks; indextransformation algorithms; linear algebra framework; Gray code encoding; decoding;matrix transpose; bit reversal; vector reversal; shuffles; hypercube multiprocessors;hypercube communications algorithms; Gauss-Jordan elimination

S. Johnsson, S. Heller and A. Edelman, "Index Transformation Algorithms in a Linear Algebra Framework," in IEEE Transactions on Parallel & Distributed Systems, vol. 5, no. , pp. 1302-1309, 1994.
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