Understanding Linear Codes for Homework

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How do you know if a code is linear.

I have only been given examples of linear codes, not what makes them linear codes.

I have to find out for homework if the product of two linear codes will be a linear code.

Eg Will C x C' be a linear code if C and C' are linear codes?

Cheers
 
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I am sure I did a search and that never came up, cheers will have a look.
 
Yes that what I know already but don't understand,

How do I relate it to my question?

Cheers
 
Just follow the definition. A code is linear because it is a linear subspace (with finite elements, or vectors). So you need to study linear subspaces (with finite elements).

Say Ci is a linear subspace, for each i = 1, 2 (which means that each Ci satisfies the 3 conditions of linear subspaces and has a finite number of elements). Does that mean that C = C1 x C2 is also a linear subspace (does C satisfy the 3 conditions of linear subspaces and have a finite number of elements, given that each of C1 and C2 does)?
 
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