Applied and Computational Mathematics Seminar
Sequential Error-Correcting Codes, by Benigno Parra-Avila (Department of Mathematics, Ohio University)
| What |
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|---|---|
| When |
Oct 22, 2007 from 04:10 pm to 05:00 pm |
| Where | Morton Hall 326 |
| Contact Name | Vardges Melkonian |
| Contact Email | vardges@math.ohiou.edu |
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SPEAKER: Benigno Parra-Avila, Department of Mathematics, Ohio University
TITLE: Sequential Error-Correcting Codes
ABSTRACT: Cyclic codes are among the most used linear block codes. Examples of cyclic codes such as the Reed-Solomon codes are staples in the field of communication and information management. Cyclic codes also play a central role in Coding Theory from a theoretic standpoint as they are precisely the ideals of certain finite rings. Other families of codes that play similar roles are the negacyclic and constacyclic codes. In this talk we introduce the new concept of (right) sequential codes which encompasses all of the previously mentioned families. We investigate the relations of this larger family with that of cyclic codes as we consider their basic properties. In particular, we consider codes that are right and left sequential (so-called bisequential codes) as well as those bisequential codes that share the property of bisequentiality with their duals. An interesting byproduct of our research is a connection between Sequential Codes, Fields of formal Laurent Series and Algebraic Extensions of Finite Fields.
