Hello,

I'm at a loss when it comes to the next step here

I've got the question:

Let C be the [6; 3] binary code with generator matrix

G =

1 1 0 0 0 0

0 1 1 0 0 0

1 1 1 1 1 1

Is C self-orthogonal? Do the codewords whose weights are divisible by

four form a subcode of C? Justify your answers.

the generator for the dual code, is the parity matrix for the code C

and a code C is self-orthgonal if

and if is a generator matrix for the [n,k] code C in standard form then is a parity check matrix for C

from this I took the matrix and got

G=

1 0 0 1 1 1

0 1 0 1 1 1

0 0 1 1 1 1

by row operations

then I get

1 1 1 1 0 0

1 1 1 0 1 0

1 1 1 0 0 1

I don't know what to do from here to show or that it's not the case

I'm also unsure of what to do about the second part of the question, where it asks if the codewords of weight divisible by 4 form a subcode

edit:

ok so I know it's not the case

C is not self orthogonal, and the codewords of weight divisible by 4 are not a subcode of C

how do I prove this?