Crossed Product Codes

• Grant number: 22/13508-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: January 28, 2023
• End date: February 27, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Francisco Cesar Polcino Milies
• Grantee: Francisco Cesar Polcino Milies
• Visiting researcher: Leroy
• Visiting researcher institution: Université d'Artois, Lens, France
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 20/16594-0 - Non commutative rings and applications, AP.TEM

Abstract

We intend to study the possible extensions of group codes to more generalones; specifically, to codes that can be realized as ideals of crossed products, a structure that extends the notion of group algebra. To do so, we expect tostudy the primitive idempotents of semisimple crossed products, determinetheir number and methods to exhibit such elements and also determine theparameters of the codes they generate. In this way it should be possible to exhibit codes that cannot be obtained by previous methods and that can bemore efficient that the ones presently available. (AU)