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What is the syndrome of the word

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Reference no: EM132407241

Answer the following questions explaining each step in each part.

Question: 1. Consider the binary code C2⊆ F6 generated by the matrix

1084_Matrix.jpg

(a) How many words does it have? List all of them.

(b) What is its length?

(c) What is its dimension? Explain youranswer.

(d) Prove that it is a cycliccode.

(e) What is its generator polynomial? Explain youranswer.

(f) What is the checkpolynomial?

(g) Give a parity check matrix ofC2.

(h) What is the minimum distance of C2? Explain your answer.

(i) How many errors can be corrected from a word of C2? Explain youranswer.

(j) What is the syndrome of the word(100110)?

(k) If the previous word has errors,explain the steps to follow to correct them and give the corrected word. If it does not have errors, prove that, indeed, it does nothave.

(l) Give an example of a word with two errors that can not be properly corrected.

Reference no: EM132407241

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