Question

Let C be the ternary [6, 4]-code with generator matrix given by G = \begin{bmatrix} 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 \end{bmatrix} . Which of the following sets are information sets for C? S?={col?,col?,col?,col?}, S? ={col?,col?,col?,col?}, S? ={col?,col?,col?,col?}

          Let C be the ternary [6, 4]-code with generator matrix given by
G = \begin{bmatrix} 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 \end{bmatrix} .
Which of the following sets are information sets for C?
S?={col?,col?,col?,col?}, S? ={col?,col?,col?,col?}, S? ={col?,col?,col?,col?}

Let C be the ternary [6, 4]-code with generator matrix given by
G =
< b m a t r i x >
.
Which of the following sets are information sets for C?
S?=col?,col?,col?,col?, S? =col?,col?,col?,col?, S? =col?,col?,col?,col?

Added by Ashley W.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Rabia Sarwar

06/14/2024

Step 1

Step 1: A set of columns of a generator matrix is an information set if the corresponding submatrix is nonsingular. Show more…

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Let C be the ternary [6, 4]-code with generator matrix given by $$G = \begin{bmatrix} 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 \end{bmatrix}.$$ Which of the following sets are information sets for C? S₁={col₁,col₂,col₃,col₄}, S₂={col₁,col₂,col₃,col₅}, S3 ={col₁,col₂,col₃,col₆}