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Cyclic Codes - Michigan State University

Cyclic Codes - Michigan State University

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Aug 01, 2010 · The matrix Ghas ncolumns and k= n rrows; so the rst row, row g 0, nishes with a string of 0’s of length k 1. Each successive row is the cyclic shift of the previous row: g i= g~ i 1, for i= 1;:::;k 1. As g(x)h(x) = xn 1, we have g 0h 0 = g(0)h(0) = 0n 1 6= 0 : In particular g 0 6= 0 (and h 0 6= 0). Therefore Gis in echelon form (although ...

  Form, Code, Cyclic, Echelon, Cyclic codes, Echelon form

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