4023f10ps8

4023f10ps8 - C in standard form. (b) Find a parity check...

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Homework #8 Due: November 10, 2010 Do the following exercises from Lax: Page 224: 2.4; Page 234: 3.5, 3.6. 1. Let C 1 and C 2 be binary linear codes having the generator matrices G 1 = 1 1 1 1 0 0 0 1 1 1 and G 2 = 2 4 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 3 5 : (a) List the codewords of C 1 and C 2 (b) Determine the minimum distance of each code. 2. Let C be the binary linear code with generator matrix 2 6 6 4 1 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 3 7 7 5 : (a) Find a generator matrix G for
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Unformatted text preview: C in standard form. (b) Find a parity check matrix H for C . (c) Determine the minimum distance d ( C ) of C . (d) How many errors can C detect? How many can it correct? 3. Recall that the 10 digit ISBN code is a 10 digit string of words in GF (11) = Z 11 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 with P 10 i =1 ix i · 0 (mod 11). Replace ? with the correct digit in the following ISBN: 368576?969. Math 4023 1...
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This document was uploaded on 12/28/2011.

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