Let a linear code have the following parity check matrix. 0 1 1 1 0 0] 1 0 0 1 0 H= 1 LO 1 1 1 a) Find its generator matrix G. b) List all the codewords by using the generator matrix found in (a). c) Find the length, dimension and minimum distance of this code.

Let a linear code have the following parity check matrix. 0 1 1 1 0 0] 1 0 0 1 0 H= 1 LO 1 1 1 a) Find its generator matrix G. b) List all the codewords by using the generator matrix found in (a). c) Find the length, dimension and minimum distance of this code.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let a linear code have the following parity check matrix.
1 1 1
H =1 1 10 0
1 0
0 .
Lo 1
1 1
0.
a) Find its generator matrix G.
b) List all the codewords by using the generator matrix found in (a).
c) Find the length, dimension and minimum distance of this code.
d) If the received vector is y =
1000111, then which codeword was likely to be
sent?
e) How many errors does this code correct?

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