{"title":"Analysis of minimal distance of AG-code associated with maximal curve of genus three","authors":"E. Malygina, Artem A. Kuninets","doi":"10.17223/20710410/58/1","DOIUrl":null,"url":null,"abstract":"A class of algebro-geometric codes associated with a maximal curve of the third kind is considered. Using the apparatus of functional fields, the type and degree of divisors involved in the construction of the code are established, under which the code is or is not an MDS code.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Prikladnaya Diskretnaya Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17223/20710410/58/1","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
A class of algebro-geometric codes associated with a maximal curve of the third kind is considered. Using the apparatus of functional fields, the type and degree of divisors involved in the construction of the code are established, under which the code is or is not an MDS code.
期刊介绍：
The scientific journal Prikladnaya Diskretnaya Matematika has been issued since 2008. It was registered by Federal Control Service in the Sphere of Communications and Mass Media (Registration Witness PI № FS 77-33762 in October 16th, in 2008). Prikladnaya Diskretnaya Matematika has been selected for coverage in Clarivate Analytics products and services. It is indexed and abstracted in SCOPUS and WoS Core Collection (Emerging Sources Citation Index). The journal is a quarterly. All the papers to be published in it are obligatorily verified by one or two specialists. The publication in the journal is free of charge and may be in Russian or in English. The topics of the journal are the following: 1.theoretical foundations of applied discrete mathematics – algebraic structures, discrete functions, combinatorial analysis, number theory, mathematical logic, information theory, systems of equations over finite fields and rings; 2.mathematical methods in cryptography – synthesis of cryptosystems, methods for cryptanalysis, pseudorandom generators, appreciation of cryptosystem security, cryptographic protocols, mathematical methods in quantum cryptography; 3.mathematical methods in steganography – synthesis of steganosystems, methods for steganoanalysis, appreciation of steganosystem security; 4.mathematical foundations of computer security – mathematical models for computer system security, mathematical methods for the analysis of the computer system security, mathematical methods for the synthesis of protected computer systems;[...]
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