Can the set of all $2^{24}$ colors be expressed as a ternary linear code? Consider the usual RGB color palette, for which each color (red, green, blue) has $256$ distinct intensities. Can the set of all $2^{24}$ colors be expressed as a ternary linear code? If so, give a basis. If not, explain why not. 


I'm confused on how to solve this because I've only worked with binary linear codes. Can somebody please walk me through it?
Hint: The number of codewords in a ternary linear code is a power of 3.

That's my best guess for the answer that the setter expects. However, the truth is you can certainly use a ternary linear code to represent all colors, you will just have a little redundancy.