Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A general decomposition theorem is given for codes over finite fields which have an automorphism of a given type. Such codes can be decomposed as direct sums of subcodes which may be vied as shorter length codes over extension fields. If such a code is self-dual, sometimes the subcodes are also. This decomposition is applied to prove that the self-dual (24, 12, 10) quaternary code has no automorphism of order 3. This decomposition is also applied to count the number of equivalent (2r, r) and (2r+2r+1) self-dual binary codes with an automorphism of prime order r. >
['W.C. Huffman']
I am writing a research paper on a idea On the (24, 12, 10) quaternary code and binary codes with an automorphism having two cycles
[{"from": "human", "value": "I am writing a research paper on a idea On the (24, 12, 10) quaternary code and binary codes with an automorphism having two cycles"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A general decomposition theorem is given for codes over finite fields which have an automorphism of a given type. Such codes can be decomposed as direct sums of subcodes which may be vied as shorter length codes over extension fields. If such a code is self-dual, sometimes the subcodes are also. This decomposition is applied to prove that the self-dual (24, 12, 10) quaternary code has no automorphism of order 3. This decomposition is also applied to count the number of equivalent (2r, r) and (2r+2r+1) self-dual binary codes with an automorphism of prime order r. >"}]