EECS 376 Lecture Notes - Lecture 7: Unit Vector, Hamming Code, Venn Diagram
20 Jun 2016
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1 parity check matrix: given a generator matrix g, nd a parity check matrix h, such that hy = 0 i y is a codeword. In particular, hg = 0. (h = 0 satis es this property. H, the h that captures all the parity check tests, which is an h of maximum rank. : if the generator matrix g for an [n, k, d]-ecc is in standard form then the parity matrix standard form is. Then hg = a a = 0. In fact, h is maximal, though we won"t prove this. H = (cid:2) a|in k(cid:3: if g is not in standard form, it can be brought into standard form by using elementary. Column operations, the columnwise-version of gaussian row elimination used to solve systems of equations: note that if the set is modular 2 then -a = a, example. Consider the following generator matrix for a [6,3,3] code.
