<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2019000100153</article-id>
<article-id pub-id-type="doi">10.18273/revint.v37n1-2019008.</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Group algebras and coding theory: a short survey]]></article-title>
<article-title xml:lang="es"><![CDATA[Álgebras de grupo y teoría de códigos: una breve reseña]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Polcino Mllies]]></surname>
<given-names><![CDATA[César]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade de São Paulo Instituto de Matemática e Estatística ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Brazil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<volume>37</volume>
<numero>1</numero>
<fpage>153</fpage>
<lpage>166</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2019000100153&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2019000100153&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2019000100153&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We study codes constructed from ideals in group algebras and we are particularly interested in their dimensions and weights. First we introduced a special kind of idempotents and study the ideals they generate. We use this information to show that there exist abelian non-cyclic groups that give codes which are more convenient than the cyclic ones. Finally, we discuss briefly some facts about non-abelian codes. MSC2010: 16S34, 20C05, 94B15.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Estudiamos códigos construidos a partir de ideales de álgebras de grupo y estamos particularmente interesados en sus dimensiones y pesos. Introducimos inicialmente un tipo especial de idempotentes y estudiamos los ideales que generan. Usamos esta información para mostrar que existen grupos abelianos no cíclicos que son más convenientes que los cíclicos. Finalmente, discutimos brevemente algunos resultados sobre códigos no abelianos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[code]]></kwd>
<kwd lng="en"><![CDATA[Hamming distance]]></kwd>
<kwd lng="en"><![CDATA[weight]]></kwd>
<kwd lng="en"><![CDATA[group algebra]]></kwd>
<kwd lng="en"><![CDATA[ideal]]></kwd>
<kwd lng="en"><![CDATA[group code]]></kwd>
<kwd lng="es"><![CDATA[códigos]]></kwd>
<kwd lng="es"><![CDATA[distancia de Hamming]]></kwd>
<kwd lng="es"><![CDATA[peso]]></kwd>
<kwd lng="es"><![CDATA[álgebra de grupo]]></kwd>
<kwd lng="es"><![CDATA[ideal]]></kwd>
<kwd lng="es"><![CDATA[código de grupo]]></kwd>
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<surname><![CDATA[Thompson]]></surname>
<given-names><![CDATA[T.M]]></given-names>
</name>
</person-group>
<source><![CDATA[From error-correcting codes through sphere packings to simple groups, Carus Mathematical Monographs 21, Mathematical Association of America]]></source>
<year>1983</year>
<publisher-loc><![CDATA[Washington ]]></publisher-loc>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
