中意绿色能源试验室建设事宜.ppt

* For the researches on Reed Muller codes, see Yanling Chen’s paper (2010 IT). Maybe LDPC … in the future ? * To deal with the big problem, we consider cyclic code and cyclic subcode. GOOD NEWS: For general linear code, the corresponding problem is not easy since few algebraic structures are left in its subcodes. But for cyclic codes and subcodes, it looks OK * GOOD NEWS: For general fixed linear code, the lengths of all the distance profiles are the same as the rank of the code. For cyclic subcode chain, the lengths of the distance profiles are also the same. * GOOD NEWS: For general fixed linear code, the dimension profiles are the same, and any discussion is under the condition of the same dimension profile. It is unlucky that, the dimension profiles of the cyclic subcode chains are not the same, so we cannot discuss the distance profiles directly. But by classifying the set of cyclic subcode chains, we can deal with the problem. * Mathematics Description * Classification on the Cyclic Subcode Chains * 1 The length of its cyclic subcode chains is and J(ms) is the number of the minimal polynomials with degree ms in the factors of the generator polynomial. * 2 The number of its cyclic subcode chains is 3 The number of the chains in each class is: * 4 The number of the classes is: 5 For the special case n=qm-1, we have where is the Mobius function. * Example: The number of its cyclic subcode chains is 24 The length of its cyclic subcode chains is 4 The number of the chains in each class is 2 The number of the classes is 12 * * * For new results about the ODP of cyclic codes, please refer to our manuscript on the punctured Reed Muller codes. * 感谢各位专家的莅临指导！ * Yuan Luo Xi’an Jan. 2013 Optimum Distance Profiles of Linear Block Codes Shanghai Jiao Tong University Hamming Distance Codeword with Long Length or Short Length One way is: Hamming distance, generalized Hamming Distance, … Another Direction is: Hamming distance, distance profile, … Backg