{"title":"A method to find the volume of a sphere in the Lee metric, and its applications","authors":"Sagnik Bhattacharya, Adrish Banerjee","doi":"10.1109/ITA50056.2020.9244935","DOIUrl":null,"url":null,"abstract":"We develop general techniques to bound the size of the balls of a given radius r for q-ary discrete metrics, using the generating function for the metric and Sanov’s theorem, that reduces to the known bound in the case of the Hamming metric and gives us a new bound in the case of the Lee metric. We use the techniques developed to find Hamming, Elias-Bassalygo and Gilbert-Varshamov bounds for the Lee metric.","PeriodicalId":137257,"journal":{"name":"2020 Information Theory and Applications Workshop (ITA)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2020 Information Theory and Applications Workshop (ITA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITA50056.2020.9244935","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We develop general techniques to bound the size of the balls of a given radius r for q-ary discrete metrics, using the generating function for the metric and Sanov’s theorem, that reduces to the known bound in the case of the Hamming metric and gives us a new bound in the case of the Lee metric. We use the techniques developed to find Hamming, Elias-Bassalygo and Gilbert-Varshamov bounds for the Lee metric.
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