Let a linear code have the following parity check matrix. [1 0 1 1 1 0] H = |1 1 1 o 0 1 0 lo 1 1 1 0 0 1l 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?

Let a linear code have the following parity check matrix. [1 0 1 1 1 0] H = |1 1 1 o 0 1 0 lo 1 1 1 0 0 1l 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?

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section2.1: Matrices And Vectors

Problem 5P

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