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solution - EE 421 Fall 2010 Homework 2 - Solutions Problem...

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EE 421 – Fall 2010 Homework 2 - Solutions Problem 1 Consider the binary code composed by the 4 codewords: C={c1=000000, c2=100100, c3=010010, c4=001001} Is this code linear? No, the code is not linear. For instance, c2+c3= 100100+010010=110110 does not belong to the code What is its minimum distance? d(c1,c2)=2, d(c1,c3)=2, d(c1,c4)=2, d(c2,c3)=4, d(c2,c4)=4, d(c3,c4)=4 Æ dmin=2 Problem 2 Find the lower bound on required minimum distance for the following codes: A single-error correcting binary code : t=1 Æ dmin=3 A triple-error correcting binary code: t=3 Æ dmin=7 A six-error detecting binary code: e=6 Æ dmin=7 since = 2 1 min d t and 1 min = d e Problem 3 Find the length n, the dimension k, the minimum distance, the generating (encoding) matrix and a possible base for the linear code defined by the following parity check matrix: = 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 H
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solution - EE 421 Fall 2010 Homework 2 - Solutions Problem...

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