A Note on Linear Codes over Semigroup Rings
| dc.contributor.author | Andrade, Antonio Aparecido de [UNESP] | |
| dc.contributor.author | Shah, Tariq | |
| dc.contributor.author | Khan, Atlas | |
| dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
| dc.contributor.institution | Quaid-i-Azam University | |
| dc.date.accessioned | 2015-04-27T11:55:57Z | |
| dc.date.available | 2015-04-27T11:55:57Z | |
| dc.date.issued | 2011 | |
| dc.description.abstract | In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 1 3Z0] instead of the polynomial ring B[X; Z0], where B is a finite commutative ring with identity, and for these constructions we improve the several results of [1]. After this, we present a decoding principle for BCH, alternant and Goppa codes which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight t ≤ r/2, i.e., whose minimum Hamming distance is r + 1. | en |
| dc.description.affiliation | Universidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, Brasil | |
| dc.description.affiliationUnesp | Universidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Matemática, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, Brasil | |
| dc.format.extent | 79-89 | |
| dc.identifier.citation | TEMA. Tendências em Matemática Aplicada e Computacional, v. 12, n. 2, p. 79-89, 2011. | |
| dc.identifier.doi | 10.5540/tema.2011.012.02.0079 | |
| dc.identifier.issn | 1677-1966 | |
| dc.identifier.lattes | 8940498347481982 | |
| dc.identifier.uri | http://hdl.handle.net/11449/122690 | |
| dc.language.iso | eng | |
| dc.relation.ispartof | TEMA. Tendências em Matemática Aplicada e Computacional | |
| dc.rights.accessRights | Acesso restrito | |
| dc.source | Currículo Lattes | |
| dc.subject | Semigroup ring | en |
| dc.subject | BCH code | en |
| dc.subject | Alternant code | en |
| dc.subject | Goppa code | en |
| dc.subject | Srivastava code | en |
| dc.title | A Note on Linear Codes over Semigroup Rings | en |
| dc.type | Artigo | |
| unesp.author.lattes | 8940498347481982[1] | |
| unesp.author.orcid | 0000-0001-6452-2236[1] | |
| unesp.campus | Universidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Preto | pt |