Consider a linear code over GF(7) determined by the parity check matrix[1 1 1 1 1 11 2 3 4 5 6](a) Find a parity check matrix in standard form, and find a generator matrixaccordingly.(b) Suppose you received [010601]. Assuming no more than one error has occurred,decode it.(c) Suppose you receive [111111]. Does it have no more than 1 error?(d) What is the distance of this code?

Consider a linear code over GF(7) determined by the parity check matrix[1 1 1 1 1 11 2 3 4 5 6](a) Find a parity check matrix in standard form, and find a generator matrixaccordingly.(b) Suppose you received [010601]. Assuming no more than one error has occurred,decode it.(c) Suppose you receive [111111]. Does it have no more than 1 error?(d) What is the 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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Consider a linear code over GF(7) determined by the parity check matrix[1 1 1 1 1 11 2 3 4 5 6](a) Find a parity check matrix in standard form, and find a generator matrixaccordingly.(b) Suppose you received [010601]. Assuming no more than one error has occurred,decode it.(c) Suppose you receive [111111]. Does it have no more than 1 error?(d) What is the distance of this code?
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