1. Linear binary codes arising from finite groups
- Author
-
Yannick Saouter, Département Electronique (ELEC), Université européenne de Bretagne - European University of Brittany (UEB)-Institut Mines-Télécom [Paris] (IMT)-Télécom Bretagne, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (UMR 3192) (Lab-STICC), Université européenne de Bretagne - European University of Brittany (UEB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), and Université de Brest (UBO)-Télécom Bretagne-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Discrete mathematics ,Block code ,Reed–Muller code ,020206 networking & telecommunications ,010103 numerical & computational mathematics ,02 engineering and technology ,Locally decodable code ,Luby transform code ,01 natural sciences ,Linear code ,Expander code ,[SPI.TRON]Engineering Sciences [physics]/Electronics ,Algebra ,Group code ,0202 electrical engineering, electronic engineering, information engineering ,Tornado code ,0101 mathematics ,[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing ,Mathematics ,Computer Science::Information Theory - Abstract
International audience; In this paper, we describe constructions of majority logic decodable codes which stem out description of finite groups. To this end, we generalize some previous studies of Tonchev, Key and Moori on codes from finite groups. We also extend some results obtained by Rudolph for majority logic decodable codes. Finally, we describe applications of these codes in the area of soft-decoding techniques.
- Published
- 2010