Question: 3. A (linear, binary) error-correcting code is a certain subspace of F. One example is ker ( H), where H : F? - F, is

3. A (linear, binary) error-correcting code is a certain subspace of F. One example is ker ( H), where H : F? - F, is defined by atctetg H(a, b, c, d, e, f,g) = b+ctf+g dte+f +g. (a) Show that if U E ker(H ) and 7 0, then U has at least 3 non-zero components. (b) Explain why two distinct vectors in ker(H) must differ in at least 3 components. Hint: consider 7 + w.]

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