{"title":"Decomposition of polynomials using the shift-composition operation","authors":"V. Nozdrunov","doi":"10.1515/dma-2023-0009","DOIUrl":null,"url":null,"abstract":"Abstract V. I. Solodovnikov had employed the shift-composition operation to investigate homomorphisms of shift registers into linear automata; in his papers, conditions for the absence of nontrivial inner homomorphisms of shift registers were derived. An essential role was played by the condition of linearity of the left component of the shift-composition operation in the corresponding polynomial decomposition. In this paper we consider the case where the left component is a function belonging to a wider class, which includes the class of linear functions.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"33 1","pages":"87 - 97"},"PeriodicalIF":0.3000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/dma-2023-0009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract V. I. Solodovnikov had employed the shift-composition operation to investigate homomorphisms of shift registers into linear automata; in his papers, conditions for the absence of nontrivial inner homomorphisms of shift registers were derived. An essential role was played by the condition of linearity of the left component of the shift-composition operation in the corresponding polynomial decomposition. In this paper we consider the case where the left component is a function belonging to a wider class, which includes the class of linear functions.
期刊介绍:
The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.