Question: Suppose that C is the binary [7,3] code with generator matrix (1 0 0 1 1 1 0 0 1 0 0 1 1 1

Suppose that C is the binary [7,3] code with generator matrix

(1 0 0 1 1 1 0

0 1 0 0 1 1 1 =G.

0 0 1 1 0 1 1)

List all elements of C and hence find the minimum distance d(C). How many errors e can C correct?

Suppose that the word y = (1 0 0 0 1 1 0) is received.

i. Calculate the coset containing y.

ii. Find the coset leader for y.

iii. Assuming that y contains no more errors than C can correct, use coset leader decoding to find the codeword which was transmitted

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