(a) Assume a flash memory can have 6 levels {0, 1, 2, 3, 4, 5} and...

 

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(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. {0, 1, 2, 3, 4}. Find the maximum number of codewords of a perfect error correcting code with legth one and two. Show the codewords. (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. {0, 1, 2, 3, 4}. Find the maximum number of codewords of a perfect error correcting code with legth one and two. Show the codewords.

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