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On majority-logic decoding for duals of primitive polynomial codes
- Source :
- IEEE Transactions on Information Theory. 17:322-331
- Publication Year :
- 1971
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 1971.
-
Abstract
- The class of polynomial codes introduced by Kasami et al. has considerable inherent algebraic and geometric structure. It has been shown that this class of codes and their dual codes contain many important classes of cyclic codes as subclasses, such as BCH codes, Reed-Solomon codes, generalized Reed-Muller codes, projective geometry codes, and Euclidean geometry codes. The purpose of this paper is to investigate further properties of polynomial codes and their duals. First, majority-logic decoding for the duals of certain primitive polynomial codes is considered. Two methods of forming nonorthogonal parity-check sums are presented. Second, the maximality of Euclidean geometry codes is proved. The roots of the generator polynomial of an Euclidean geometry code are specified.
- Subjects :
- Discrete mathematics
Block code
Concatenated error correction code
Reed–Muller code
Data_CODINGANDINFORMATIONTHEORY
Library and Information Sciences
Luby transform code
Linear code
Expander code
Computer Science Applications
Combinatorics
Reed–Solomon error correction
BCH code
Computer Science::Information Theory
Information Systems
Mathematics
Subjects
Details
- ISSN :
- 00189448
- Volume :
- 17
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Information Theory
- Accession number :
- edsair.doi...........c955d474c7d2b15ea41cea484aa43e91