{"title":"周期序列线性复杂度的矩阵代数","authors":"Chingwo Ma","doi":"10.1109/ISIC.2012.6449697","DOIUrl":null,"url":null,"abstract":"A matrix algebra is presented for the linear complexity of periodic sequences over finite fields. An algorithm is developed to compute the rank of the circulant matrices and it can be viewed as a matrix formulation of Blackburn's algorithm. The rank-nullity property is shown precisely between the pseudocirculant matrices and the Hasse matrices.","PeriodicalId":393653,"journal":{"name":"2012 International Conference on Information Security and Intelligent Control","volume":"120 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A matrix algebra for the linear complexity of periodic sequences\",\"authors\":\"Chingwo Ma\",\"doi\":\"10.1109/ISIC.2012.6449697\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A matrix algebra is presented for the linear complexity of periodic sequences over finite fields. An algorithm is developed to compute the rank of the circulant matrices and it can be viewed as a matrix formulation of Blackburn's algorithm. The rank-nullity property is shown precisely between the pseudocirculant matrices and the Hasse matrices.\",\"PeriodicalId\":393653,\"journal\":{\"name\":\"2012 International Conference on Information Security and Intelligent Control\",\"volume\":\"120 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 International Conference on Information Security and Intelligent Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIC.2012.6449697\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 International Conference on Information Security and Intelligent Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIC.2012.6449697","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A matrix algebra for the linear complexity of periodic sequences
A matrix algebra is presented for the linear complexity of periodic sequences over finite fields. An algorithm is developed to compute the rank of the circulant matrices and it can be viewed as a matrix formulation of Blackburn's algorithm. The rank-nullity property is shown precisely between the pseudocirculant matrices and the Hasse matrices.
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