Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let a binary Reed-Muller code RM(s;m) of length n be used on a memoryless channel with an input alphabet ±1 and a real-valued output ℝ. Given a received vector y in ℝ n ;  define its generalized distance T to any codeword c as the sum ∑|y j|  taken over all positions j, in which vectors y, c have opposite signs.  then consider the list ℒ T  of codewords located within distance T from the received vector y and estimate the size L T  of this list using the generalized Johnson bound. For any RM code RM(s;m) of fixed order s, the algorithm is proposed that performs list decoding beyond the error-correcting radius with linear complexity in length n and retrieves the code list ℒ T  with complexity of order nsL T  for any decoding radius T within the generalized Johnson bound.
['Ilya Dumer', 'Grigory Kabatiansky', 'Cédric Tavernier']
I am writing a research paper on a idea Soft-decision list decoding of Reed-Muller codes with linear complexity
[{"from": "human", "value": "I am writing a research paper on a idea Soft-decision list decoding of Reed-Muller codes with linear complexity"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let a binary Reed-Muller code RM(s;m) of length n be used on a memoryless channel with an input alphabet \u00b11 and a real-valued output \u211d. Given a received vector y in \u211d n ;  define its generalized distance T to any codeword c as the sum \u2211|y j|  taken over all positions j, in which vectors y, c have opposite signs.  then consider the list \u2112 T  of codewords located within distance T from the received vector y and estimate the size L T  of this list using the generalized Johnson bound. For any RM code RM(s;m) of fixed order s, the algorithm is proposed that performs list decoding beyond the error-correcting radius with linear complexity in length n and retrieves the code list \u2112 T  with complexity of order nsL T  for any decoding radius T within the generalized Johnson bound."}]