Question: Consider the following ternary code that associates to (x, y) the codeword (x, y, x + y, x + 2y), where x, y {0,1, 2}

Consider the following ternary code that associates to (x, y) the

Consider the following ternary code that associates to (x, y) the codeword (x, y, x + y, x + 2y), where x, y {0,1, 2} and addition and multiplication are modulo 3. (a) Show that this code can correct any possible two erasures? (hint: you can go over all possi- bilities) (b) Deduce the minimum distance of this code. (c) How many errors can this code detect? correct? (d) Is this code a perfect code? Is it MDS? (e) Suppose this code is used on a Binary Erasure Channel. At its output the following is received (?, ?,0,2). What was the transmitted codeword. Consider the following ternary code that associates to (x, y) the codeword (x, y, x + y, x + 2y), where x, y {0,1, 2} and addition and multiplication are modulo 3. (a) Show that this code can correct any possible two erasures? (hint: you can go over all possi- bilities) (b) Deduce the minimum distance of this code. (c) How many errors can this code detect? correct? (d) Is this code a perfect code? Is it MDS? (e) Suppose this code is used on a Binary Erasure Channel. At its output the following is received (?, ?,0,2). What was the transmitted codeword

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