{"title":"一类四元弯曲函数的吉布斯刻划","authors":"R. Stankovic, M. Stankovic, J. Astola, C. Moraga","doi":"10.1109/ISMVL.2017.39","DOIUrl":null,"url":null,"abstract":"Bent functions generalized to the alphabet Zq, the ring of integers modulo q, are interesting not just in the realm of multiple-valued functions, but have some applications in the binary environment. The case q = 4, i.e., quaternary bent functions, are of a particular interest due to a simple relationship to binary functions. We consider the possibilities for characterization of quaternary bent functions in terms of the Gibbs derivatives defined with respect to the Reed-Muller-Fourier (RMF) transform for q-valued functions. It is shown that quaternary bent functions can be split into classes of functions sharing the same values for their Gibbs derivatives.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Towards the Gibbs Characterization of a Class of Quaternary Bent Functions\",\"authors\":\"R. Stankovic, M. Stankovic, J. Astola, C. Moraga\",\"doi\":\"10.1109/ISMVL.2017.39\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Bent functions generalized to the alphabet Zq, the ring of integers modulo q, are interesting not just in the realm of multiple-valued functions, but have some applications in the binary environment. The case q = 4, i.e., quaternary bent functions, are of a particular interest due to a simple relationship to binary functions. We consider the possibilities for characterization of quaternary bent functions in terms of the Gibbs derivatives defined with respect to the Reed-Muller-Fourier (RMF) transform for q-valued functions. It is shown that quaternary bent functions can be split into classes of functions sharing the same values for their Gibbs derivatives.\",\"PeriodicalId\":393724,\"journal\":{\"name\":\"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2017.39\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2017.39","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Towards the Gibbs Characterization of a Class of Quaternary Bent Functions
Bent functions generalized to the alphabet Zq, the ring of integers modulo q, are interesting not just in the realm of multiple-valued functions, but have some applications in the binary environment. The case q = 4, i.e., quaternary bent functions, are of a particular interest due to a simple relationship to binary functions. We consider the possibilities for characterization of quaternary bent functions in terms of the Gibbs derivatives defined with respect to the Reed-Muller-Fourier (RMF) transform for q-valued functions. It is shown that quaternary bent functions can be split into classes of functions sharing the same values for their Gibbs derivatives.