Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   extend the relation beten convolutional codes and linear systems over finite fields to certain commutative rings through first order representations .  introduce the definition of rings with representations as those for which these representations always exist, and  show that finite products of finite fields belong to this class.  develop the input/state/output representations for convolutional codes over these rings, and  show how to use them to construct observable convolutional codes as in the classical case.
['Miguel V. Carriegos', 'Noemí DeCastro-García', 'Ángel Luis Muñoz Castañeda']
I am writing a research paper on a idea Linear representations of convolutional codes over rings
[{"from": "human", "value": "I am writing a research paper on a idea Linear representations of convolutional codes over rings"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   extend the relation beten convolutional codes and linear systems over finite fields to certain commutative rings through first order representations .  introduce the definition of rings with representations as those for which these representations always exist, and  show that finite products of finite fields belong to this class.  develop the input/state/output representations for convolutional codes over these rings, and  show how to use them to construct observable convolutional codes as in the classical case."}]