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!...
View Full Document
- Fall '08
- ISBN, International Standard Book Number, book Number, nine digits, Parity-check matrix, double-error correcting code