For a (8,3) code and the systematic cyclic code generator 1+X+X^4+X^5. Show all

Question

For a (8,3) code and the systematic cyclic code generator 1+X+X^4+X^5. Show all work.

a) Determine the code words for 4 of the possible messages.

b) What is the error detection and error correction capability of this code.

c) Define an eror correction look-up table for all correctable errors per result in part b.

d) Find the syndrome of the received vector 00010101. Correct the received code using the look-up table from part c.

e) What is the original message based on your result in part d.

f) What is the probability of an undetected error if p +10^-3.

Explanation / Answer

code: 1+x

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