Coding and cryptography

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

For each of m = 1, 2, 3, 4, and 9 write down a ternary linear code of length 2 containing m codewords, or explain why there is no such code. In general for what m does there exist a ternary linear code with m codewords? Justify your answer, referencing any research you have done. Marks will be deducted for failure to reference research correctly using the Harvard system.

Færdigheder: Matematik, Coding, Kryptografi

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