This question is about how many code words there can be in a ternary linear code.Note that m is the number of code words, not the length of the code.

A ternary code uses the symbols 0, 1 and 2 with the properties that 1+1=2, 1+2 = 0,and 2+2 =1. Note that m is the number of code words, not the length of the code. For each of m = 1, 2, 3, 4, and 9 write down a ternary linear code of length 2containing m code words, or explain why there is no such code. In general, for what m does there exist a ternary linear code with m code words?