Using the Structure of Subfields in the Construction of Goppa Codes and Extended Goppa Codes

Autor:	Martin Tomlinson, Sergey Bezzateev, Mubarak Jibril, Mohammed Zaki Ahmed, Marcel Ambroze
Rok vydání:	2015
Předmět:	Block code Discrete mathematics Concatenated error correction code Reed–Muller code Library and Information Sciences Linear code Expander code Computer Science Applications Combinatorics Group code Goppa code Hamming code Computer Science::Cryptography and Security Information Systems Mathematics
Zdroj:	IEEE Transactions on Information Theory. 61:3214-3224
ISSN:	1557-9654 0018-9448
DOI:	10.1109/tit.2015.2419613
Popis:	It is shown that for some location sets and some integral multiple power Galois fields that some new general subclasses of Goppa codes may be defined which have improved lower bounds to code dimension and minimum distance compared with ordinary Goppa codes. Some previously published results are shown to be particular cases of these general subclasses of codes. A new subclass of reversible Goppa codes is also presented. Examples of code construction for these subclasses, demonstrating the improved code parameters, are presented for both non binary and binary codes.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::f6c0a13835eaf2c3b92a39b8610849b3 https://doi.org/10.1109/tit.2015.2419613 Zobrazit plný text záznamu