Exercise 2.10. Let C be a (n, k, d) binary linear code. Define the extended code to be n+1 C = (C₁,..., C₁, Cn+1): (C₁,..., Cn) E C and -{(es..... [a=0} Write generator and parity check matrices of the extended code in terms of generator and parity check matrices of the original code. Assume d odd. What is the minimal distance of the extended code?

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Exercise 2.10. Let C be a (n, k, d) binary linear code. Define the extended code to be
n+1
C = { (C1,.
Cns Gn+1) : (c1,...,Cm) e C and Ea=0}
i=1
Write generator and parity check matrices of the extended code in terms of generator and
parity check matrices of the original code. Assume d odd. What is the minimal distance
of the extended code?
Transcribed Image Text:Exercise 2.10. Let C be a (n, k, d) binary linear code. Define the extended code to be n+1 C = { (C1,. Cns Gn+1) : (c1,...,Cm) e C and Ea=0} i=1 Write generator and parity check matrices of the extended code in terms of generator and parity check matrices of the original code. Assume d odd. What is the minimal distance of the extended code?
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