Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices,  can formulate a minimum Euclidian distance decoding problem for the proposed class of permutation codes as a linear programming (LP) problem. The main feature of this novel class of permutation codes, called LP decodable permutation codes, is this LP decodability. It is demonstrated that the LP decoding performance of the proposed class of permutation codes is characterized by the vertices of the code polytope of the code. In addition, based on a probabilistic method, several theoretical results for randomly constrained permutation codes are derived.
['Tadashi Wadayama', 'Manabu Hagiwara']
I am writing a research paper on a idea LP decodable permutation codes based on linearly constrained permutation matrices
[{"from": "human", "value": "I am writing a research paper on a idea LP decodable permutation codes based on linearly constrained permutation matrices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices,  can formulate a minimum Euclidian distance decoding problem for the proposed class of permutation codes as a linear programming (LP) problem. The main feature of this novel class of permutation codes, called LP decodable permutation codes, is this LP decodability. It is demonstrated that the LP decoding performance of the proposed class of permutation codes is characterized by the vertices of the code polytope of the code. In addition, based on a probabilistic method, several theoretical results for randomly constrained permutation codes are derived."}]