What are the possible values of n

Reference no: EM133258727

In this question we consider binary linear codes of length n, where n is a positive integer greater than 1.

(a) For this part of the question, assume n is odd. We consider a perfect code C of length n having dimension k = 1.
(i) Explain why such a perfect code exists.
(ii) What is the minimum distance d between distinct code words? Explain your answer.
(iii) What is the nunber t of correctible errors? Explain your answer.
(iv) How big are the t-spheres centred on the code words? Explain your answer.

(b) Assume instead that n is even. Does there exist a perfect code of length n having dimension k = 1? Explain your answer fully.

(c) Let C be a Hamming code of length n.
(i) What are the possible values of n? Explain your answer.
(ii) Explain why C is a perfect code.

Reference no: EM133258727

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