{"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}
引用次数: 1
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.
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