{"title":"特征二有限域上Kloosterman和的可整除性","authors":"P. Charpin, T. Helleseth, V. Zinoviev","doi":"10.1109/ISIT.2008.4595463","DOIUrl":null,"url":null,"abstract":"Let K(a) be the so-called classical Kloosterman sums over F2m, where m is even. In this paper, we compute K(a) modulo 24, completing our previous results for odd m. We extensively study the links between K(a) and other exponential sums, in particular with the cubic sums. We point out (as we did for odd m) that the values K(a) are related with cosets of weight 4 of primitive narrow sense extended BCH codes of length n = 2m and minimum distance 8.","PeriodicalId":194674,"journal":{"name":"2008 IEEE International Symposium on Information Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"Divisibility properties of Kloosterman sums over finite fields of characteristic two\",\"authors\":\"P. Charpin, T. Helleseth, V. Zinoviev\",\"doi\":\"10.1109/ISIT.2008.4595463\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let K(a) be the so-called classical Kloosterman sums over F2m, where m is even. In this paper, we compute K(a) modulo 24, completing our previous results for odd m. We extensively study the links between K(a) and other exponential sums, in particular with the cubic sums. We point out (as we did for odd m) that the values K(a) are related with cosets of weight 4 of primitive narrow sense extended BCH codes of length n = 2m and minimum distance 8.\",\"PeriodicalId\":194674,\"journal\":{\"name\":\"2008 IEEE International Symposium on Information Theory\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-07-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 IEEE International Symposium on Information Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2008.4595463\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 IEEE International Symposium on Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2008.4595463","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Divisibility properties of Kloosterman sums over finite fields of characteristic two
Let K(a) be the so-called classical Kloosterman sums over F2m, where m is even. In this paper, we compute K(a) modulo 24, completing our previous results for odd m. We extensively study the links between K(a) and other exponential sums, in particular with the cubic sums. We point out (as we did for odd m) that the values K(a) are related with cosets of weight 4 of primitive narrow sense extended BCH codes of length n = 2m and minimum distance 8.
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