{"title":"Spectral analysis of high order correlation immune functions","authors":"Y. Tarannikov, D. Kirienko","doi":"10.1109/ISIT.2001.935932","DOIUrl":null,"url":null,"abstract":"We consider F/sub 2//sup n/, the vector space of n-tuples of elements from F/sub 2/. An n-variable Boolean function is a map from F/sub 2//sup n/ into F/sub 2/. The weight of a vector x is the number of ones in x and is denoted by |x|. The weight wt(f) of a function f on F/sub 2//sup n/ is the number of vectors x on F/sub 2//sup n/ such that f(x)=1. A function f is said to be balance if wt(f)=wt(f/spl oplus/1)=2/sup n-1/. A subfunction of the Boolean function f is a function f/spl acute/ obtained by substituting some constants for some variables in f.","PeriodicalId":433761,"journal":{"name":"Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)","volume":"171 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2001.935932","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 19
Abstract
We consider F/sub 2//sup n/, the vector space of n-tuples of elements from F/sub 2/. An n-variable Boolean function is a map from F/sub 2//sup n/ into F/sub 2/. The weight of a vector x is the number of ones in x and is denoted by |x|. The weight wt(f) of a function f on F/sub 2//sup n/ is the number of vectors x on F/sub 2//sup n/ such that f(x)=1. A function f is said to be balance if wt(f)=wt(f/spl oplus/1)=2/sup n-1/. A subfunction of the Boolean function f is a function f/spl acute/ obtained by substituting some constants for some variables in f.
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