(code design for flash memory) (a) Assume a flash memory can have 6 levels {0,1,2,3,4,5}^ and the errors can be of limited value of magnitude +1 (i.e. a digit at level i can change to level (i + 1) (mod 6)). With one digit we can choose {0, 2,4) as the codewords to have a perfect error correcting code of limited magnitude +1. With two digits, what is the maximum number codewords in a limited mag- nitude +1 perfect error correcting code? Construct a code achieving this bound (b) Assume the number of levels is 5, i.e. 10,1,2,3,4). Find the maximum number of codewords of a perfect error correcting code with legth one and two. Show the codewords