{"title":"基于最快变换的GF(3)上的多项式展开式","authors":"B. Falkowski, Cheng Fu","doi":"10.1109/ISMVL.2003.1201382","DOIUrl":null,"url":null,"abstract":"A new fastest Linearly Independent (LI) transforms over GF(3) and its corresponding polynomial expansions have been introduced. The number of required additions and multiplications in new LI transform is advantageous when compared with ternary Reed-Muller transform, which was previously known as the most efficient transform over GF(3). This paper discusses various properties of these fastest LI transforms and their corresponding polynomial expansions over GF(3) as well as their comparison with ternary Reed-Muller transform and its implementation in hardware.","PeriodicalId":434515,"journal":{"name":"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.","volume":"65 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2003-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Polynomial expansions over GF(3) based on fastest transformation\",\"authors\":\"B. Falkowski, Cheng Fu\",\"doi\":\"10.1109/ISMVL.2003.1201382\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new fastest Linearly Independent (LI) transforms over GF(3) and its corresponding polynomial expansions have been introduced. The number of required additions and multiplications in new LI transform is advantageous when compared with ternary Reed-Muller transform, which was previously known as the most efficient transform over GF(3). This paper discusses various properties of these fastest LI transforms and their corresponding polynomial expansions over GF(3) as well as their comparison with ternary Reed-Muller transform and its implementation in hardware.\",\"PeriodicalId\":434515,\"journal\":{\"name\":\"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.\",\"volume\":\"65 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2003-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2003.1201382\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2003.1201382","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Polynomial expansions over GF(3) based on fastest transformation
A new fastest Linearly Independent (LI) transforms over GF(3) and its corresponding polynomial expansions have been introduced. The number of required additions and multiplications in new LI transform is advantageous when compared with ternary Reed-Muller transform, which was previously known as the most efficient transform over GF(3). This paper discusses various properties of these fastest LI transforms and their corresponding polynomial expansions over GF(3) as well as their comparison with ternary Reed-Muller transform and its implementation in hardware.
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