{"title":"复汉明空间的多项式系统","authors":"V. Levenshtein","doi":"10.1109/ISIT.2004.1365395","DOIUrl":null,"url":null,"abstract":"It is known that polynomials f(t), such that the matrix f(rho(x,y)) with the Hamming distance rho(x,y) between vectors x=(x <sub>1</sub>,...,x<sub>n</sub>) and y=(y<sub>1</sub>,...,y<sub>n</sub>) is nonnegative definite, are described with the help of the system of Krawtchouk polynomials. In the paper the question on the existence of a similar system of polynomials is considered when the function rho(x,y) is not the Hamming distance","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A system of polynomials for the complex hamming spaces\",\"authors\":\"V. Levenshtein\",\"doi\":\"10.1109/ISIT.2004.1365395\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is known that polynomials f(t), such that the matrix f(rho(x,y)) with the Hamming distance rho(x,y) between vectors x=(x <sub>1</sub>,...,x<sub>n</sub>) and y=(y<sub>1</sub>,...,y<sub>n</sub>) is nonnegative definite, are described with the help of the system of Krawtchouk polynomials. In the paper the question on the existence of a similar system of polynomials is considered when the function rho(x,y) is not the Hamming distance\",\"PeriodicalId\":269907,\"journal\":{\"name\":\"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-06-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2004.1365395\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2004.1365395","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A system of polynomials for the complex hamming spaces
It is known that polynomials f(t), such that the matrix f(rho(x,y)) with the Hamming distance rho(x,y) between vectors x=(x 1,...,xn) and y=(y1,...,yn) is nonnegative definite, are described with the help of the system of Krawtchouk polynomials. In the paper the question on the existence of a similar system of polynomials is considered when the function rho(x,y) is not the Hamming distance
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