{"title":"A Testing Set for Preparata-Like Codes","authors":"A. Yu. Vasil’eva","doi":"10.1134/S1990478923020205","DOIUrl":null,"url":null,"abstract":"<p> The reconstruction of an object of a given class by its intersection with some (so-called\ntesting) set is studied. For the class, we consider Preparata-like codes, i.e., nonlinear codes of\nlength\n<span>\\( n=2^{2m}-1 \\)</span>,\n<span>\\( m=2,3,\\dots \\)</span>, with code distance 5 and twice the size of a linear code of the same length\nand distance. Conditions are determined under which the union of a few concentric spheres forms\na testing set for Preparata-like codes.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 2","pages":"427 - 432"},"PeriodicalIF":0.5800,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923020205","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The reconstruction of an object of a given class by its intersection with some (so-called
testing) set is studied. For the class, we consider Preparata-like codes, i.e., nonlinear codes of
length
\( n=2^{2m}-1 \),
\( m=2,3,\dots \), with code distance 5 and twice the size of a linear code of the same length
and distance. Conditions are determined under which the union of a few concentric spheres forms
a testing set for Preparata-like codes.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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