Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Stopping sets and stopping set distribution of a linear code are used to determine the performance of this code under iterative decoding over a binary erasure channel (BEC). Let  C  be a binary [ n , k ] linear code with parity-check matrix  H , where the rows of  H  may be dependent. A stopping set  S  of  C  with parity-check matrix  H  is a subset of column indices of  H  such that the restriction of  H  to  S  does not contain a row of ight one. The stopping set distribution { Ti ( H )} i =0 n  enumerates the number of stopping sets with size  i  of  C  with parity-check matrix  H . Note that stopping sets and stopping set distribution are related to the parity-check matrix  H  of  C . Let  H  *  be the parity-check matrix of  C  which is formed by all the nonzero codewords of its dual code  C  ⊥ . A parity-check matrix  H  is called BEC-optimal if  Ti ( H )= Ti ( H  * ),  i =0,1,...,  n  and  H  has the smallest number of rows. ,  study stopping sets, stopping set distributions and BEC-optimal parity-check matrices of binary linear codes. Using finite geometry in combinatorics,  obtain BEC-optimal parity-check matrices and then determine the stopping set distributions for the Simplex codes, the Hamming codes, the first order Reed-Muller codes, and the extended Hamming codes, which are some Reed-Muller codes or their shortening or puncturing versions.
['Yong Jiang', 'Shu-Tao Xia', 'Fang-Wei Fu']
I am writing a research paper on a idea Stopping Set Distributions of Some Reed–Muller Codes
[{"from": "human", "value": "I am writing a research paper on a idea Stopping Set Distributions of Some Reed\u2013Muller Codes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Stopping sets and stopping set distribution of a linear code are used to determine the performance of this code under iterative decoding over a binary erasure channel (BEC). Let  C  be a binary [ n , k ] linear code with parity-check matrix  H , where the rows of  H  may be dependent. A stopping set  S  of  C  with parity-check matrix  H  is a subset of column indices of  H  such that the restriction of  H  to  S  does not contain a row of ight one. The stopping set distribution { Ti ( H )} i =0 n  enumerates the number of stopping sets with size  i  of  C  with parity-check matrix  H . Note that stopping sets and stopping set distribution are related to the parity-check matrix  H  of  C . Let  H  *  be the parity-check matrix of  C  which is formed by all the nonzero codewords of its dual code  C  \u22a5 . A parity-check matrix  H  is called BEC-optimal if  Ti ( H )= Ti ( H  * ),  i =0,1,...,  n  and  H  has the smallest number of rows. ,  study stopping sets, stopping set distributions and BEC-optimal parity-check matrices of binary linear codes. Using finite geometry in combinatorics,  obtain BEC-optimal parity-check matrices and then determine the stopping set distributions for the Simplex codes, the Hamming codes, the first order Reed-Muller codes, and the extended Hamming codes, which are some Reed-Muller codes or their shortening or puncturing versions."}]