{"title":"Maximum cellular boolean functions and perfect gray codes","authors":"A. J. Goldman, B. Bender","doi":"10.6028/jres.067b.007","DOIUrl":null,"url":null,"abstract":"I. A Boolean function of n variables, considered as a subset of t he discl'cLe uni t n-cube Bn> is called cellular if each of its connected components is a face of Bn. Hammin g'~ determination of optimal binary single-error-detectin g codes is generalized to a characteri zation of all propel' cellular functions with the greatest possible number of clements . II. An analysis is made of a class of Gray codes (H amiltonian circuits on Bn) with certain special propcrti es, e.g., ad mi tting for O:Sd:Sn a parti tion in to 2n d subpaths eac h formin g a d-c1 imensional face of Bn.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1963-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6028/jres.067b.007","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
I. A Boolean function of n variables, considered as a subset of t he discl'cLe uni t n-cube Bn> is called cellular if each of its connected components is a face of Bn. Hammin g'~ determination of optimal binary single-error-detectin g codes is generalized to a characteri zation of all propel' cellular functions with the greatest possible number of clements . II. An analysis is made of a class of Gray codes (H amiltonian circuits on Bn) with certain special propcrti es, e.g., ad mi tting for O:Sd:Sn a parti tion in to 2n d subpaths eac h formin g a d-c1 imensional face of Bn.
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