{"title":"Barnes-Wall晶格的Voronoi区域Λ16","authors":"Daniel Pook-Kolb;Erik Agrell;Bruce Allen","doi":"10.1109/JSAIT.2023.3276897","DOIUrl":null,"url":null,"abstract":"We give a detailed description of the Voronoi region of the Barnes–Wall lattice \n<inline-formula> <tex-math>$\\Lambda _{16}$ </tex-math></inline-formula>\n, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"16-23"},"PeriodicalIF":0.0000,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8700143/10153947/10126076.pdf","citationCount":"3","resultStr":"{\"title\":\"The Voronoi Region of the Barnes–Wall Lattice Λ16\",\"authors\":\"Daniel Pook-Kolb;Erik Agrell;Bruce Allen\",\"doi\":\"10.1109/JSAIT.2023.3276897\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a detailed description of the Voronoi region of the Barnes–Wall lattice \\n<inline-formula> <tex-math>$\\\\Lambda _{16}$ </tex-math></inline-formula>\\n, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.\",\"PeriodicalId\":73295,\"journal\":{\"name\":\"IEEE journal on selected areas in information theory\",\"volume\":\"4 \",\"pages\":\"16-23\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://ieeexplore.ieee.org/iel7/8700143/10153947/10126076.pdf\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE journal on selected areas in information theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10126076/\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE journal on selected areas in information theory","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/10126076/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We give a detailed description of the Voronoi region of the Barnes–Wall lattice
$\Lambda _{16}$
, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.
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