{"title":"线性分组码原象在伽罗瓦环GR(pr, m)上的最小齐次距离的界","authors":"P. Solé, V. Sison","doi":"10.1109/ISIT.2007.4557510","DOIUrl":null,"url":null,"abstract":"In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(pr ,m), with respect to any basis of GR(pr, m). These bounds depend on the parameters of GR(pr , m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zpr. Examples are given of Galois ring codes that meet these bounds.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":"4 1","pages":"1971-1974"},"PeriodicalIF":0.0000,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Bounds on the Minimum Homogeneous Distance of the pr-ary Image of Linear Block Codes over the Galois Ring GR(pr, m)\",\"authors\":\"P. Solé, V. Sison\",\"doi\":\"10.1109/ISIT.2007.4557510\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(pr ,m), with respect to any basis of GR(pr, m). These bounds depend on the parameters of GR(pr , m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zpr. Examples are given of Galois ring codes that meet these bounds.\",\"PeriodicalId\":92224,\"journal\":{\"name\":\"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications\",\"volume\":\"4 1\",\"pages\":\"1971-1974\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2007.4557510\",\"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 on Information Theory and its Applications. International Symposium on Information Theory and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2007.4557510","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bounds on the Minimum Homogeneous Distance of the pr-ary Image of Linear Block Codes over the Galois Ring GR(pr, m)
In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(pr ,m), with respect to any basis of GR(pr, m). These bounds depend on the parameters of GR(pr , m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zpr. Examples are given of Galois ring codes that meet these bounds.
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