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Unformatted text preview: distance. Show that if C is maximal, then r<d (r denotes the covering radius). Let C be with the same parameters as above, over a field F, such that any lengthening of C obtained by adding one column to a [n-k,n] parity-check matrix H of C generates d-1 dependent columns in H. Show that in this case r<d-1. 4. We saw in class that each power of a primitive element a of a field F(2^m) has a representation in terms of a polynomial of degree less than m (the field element 0 excluded). If you write these polynomial expansions out for all possible consecutive powers, show that the free coefficients in the expansion form a deBruijn sequence! Start with a small example of length 8, just to convince yourself that this is true!...
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This note was uploaded on 02/08/2012 for the course ECE 556 taught by Professor Milenkovic,o during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08