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On spectral design methods for quasi-cyclic codes
- Source :
- ISIT
- Publication Year :
- 2016
- Publisher :
- IEEE, 2016.
-
Abstract
- A method is provided for constructing upper triangular square matrices over the univariate polynomial ring over a finite field, under certain constraints on the eigenvalues of the matrices. In some cases of interest, the degree of the determinant of such matrices is shown to be the smallest possible. The method is then applied to construct generator polynomial matrices of quasi-cyclic codes for correcting phased burst errors. Finally, an interpolation-based list decoding algorithm is presented for these codes, which, for a wide range of code parameters, is shown to outperform existing list decoding schemes.
- Subjects :
- Polynomial code
MathematicsofComputing_NUMERICALANALYSIS
Triangular matrix
List decoding
0102 computer and information sciences
02 engineering and technology
Library and Information Sciences
Square matrix
01 natural sciences
Matrix polynomial
Integer matrix
Matrix (mathematics)
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
0202 electrical engineering, electronic engineering, information engineering
Matrix analysis
Eigenvalues and eigenvectors
Characteristic polynomial
Mathematics
Discrete mathematics
020206 networking & telecommunications
Polynomial matrix
Matrix multiplication
Computer Science Applications
Finite field
010201 computation theory & mathematics
Algorithm
Decoding methods
Monic polynomial
Information Systems
Interpolation
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- 2016 IEEE International Symposium on Information Theory (ISIT)
- Accession number :
- edsair.doi.dedup.....1b7fec7d2d22fc099a5a41ba9d33cb8d
- Full Text :
- https://doi.org/10.1109/isit.2016.7541471