Block Codes a block code is systematic if every codeword can be broken into a data part and a redundant part Previous (6, 3 )code was systematic Definitions: Given XE [O, 1]n, the Hamming Weight of X is the number of 1s in X Given X, Y in (o, i]n, the Hamming Distance between X&Y is the number of places in which they differ, dn(X,)=∑xe=形egh(x+ X+Y=[x⊕y,x2y2…xn由y The minimum distance of a code is the hamming distance between the two closest codewords dmin=min [dH(C1, c2)] 1C2∈cEytan Modiano Slide 11 Block Codes • A block code is systematic if every codeword can be broken into a data part and a redundant part – Previous (6,3) code was systematic Definitions: • Given X ∈ {0,1}n, the Hamming Weight of X is the number of 1’s in X • Given X, Y in {0,1}n , the Hamming Distance between X & Y is the number of places in which they differ, • The minimum distance of a code is the Hamming Distance between the two closest codewords: dmin = min {dH (C1,C2)} C1,C2 ∈ C d X Y X Y Weight X Y XY x y xy xy H i i n i n n (,) ( ) [ , ,, ] = ⊕= + += ⊕ ⊕ ⊕ = ∑ 1 1 12 2 L