{"title":"二元序列的二次复杂度","authors":"W. Penzhorn","doi":"10.1109/COMSIG.1998.736944","DOIUrl":null,"url":null,"abstract":"The linear complexity of a binary sequences is an important attribute in applications such as secure communications. In this article we introduce the concept of quadratic complexity of a binary sequences. It is shown that this complexity measure is closely linked to the theory of primitive Reed-Muller codes. Making use of the parity-check polynomial h(x) of a Reed-Muller code, a new algorithm for the computation of the quadratic complexity profile of a sequence is developed. Experimental results confirm the close resemblance between expected theoretical and practical behaviour.","PeriodicalId":294473,"journal":{"name":"Proceedings of the 1998 South African Symposium on Communications and Signal Processing-COMSIG '98 (Cat. No. 98EX214)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Quadratic complexity of binary sequences\",\"authors\":\"W. Penzhorn\",\"doi\":\"10.1109/COMSIG.1998.736944\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The linear complexity of a binary sequences is an important attribute in applications such as secure communications. In this article we introduce the concept of quadratic complexity of a binary sequences. It is shown that this complexity measure is closely linked to the theory of primitive Reed-Muller codes. Making use of the parity-check polynomial h(x) of a Reed-Muller code, a new algorithm for the computation of the quadratic complexity profile of a sequence is developed. Experimental results confirm the close resemblance between expected theoretical and practical behaviour.\",\"PeriodicalId\":294473,\"journal\":{\"name\":\"Proceedings of the 1998 South African Symposium on Communications and Signal Processing-COMSIG '98 (Cat. No. 98EX214)\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 1998 South African Symposium on Communications and Signal Processing-COMSIG '98 (Cat. No. 98EX214)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/COMSIG.1998.736944\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 1998 South African Symposium on Communications and Signal Processing-COMSIG '98 (Cat. No. 98EX214)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/COMSIG.1998.736944","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The linear complexity of a binary sequences is an important attribute in applications such as secure communications. In this article we introduce the concept of quadratic complexity of a binary sequences. It is shown that this complexity measure is closely linked to the theory of primitive Reed-Muller codes. Making use of the parity-check polynomial h(x) of a Reed-Muller code, a new algorithm for the computation of the quadratic complexity profile of a sequence is developed. Experimental results confirm the close resemblance between expected theoretical and practical behaviour.
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