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 [nk,n] paritycheck matrix H of C generates d1 dependent columns in H. Show that in this case r<d1. 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
 Milenkovic,O
 ISBN, International Standard Book Number, book Number, nine digits, Paritycheck matrix, doubleerror correcting code

Click to edit the document details