Coding and cryptography
Budget: £10 – £20 GBP
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.
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.