Mattson Solomon Transform and Algebra Codes
In this note we review some results of the first author on the structure of codes defined as subalgebras of a commutative semisimple algebra over a finite field (see Martínez-Moro in Algebra Discrete Math. 3:99–112, 2007). Generator theory and those aspects related to the theory of Gröbner bases are emphasized.
KeywordsCyclic Code Regular Representation Generator Polynomial Algebra Isomorphism Semisimple Algebra
Unable to display preview. Download preview PDF.
- D. Augot, E. Betti, and E. Orsini, An introduction to linear and cyclic codes, this volume, 2009, pp. 47–68. Google Scholar
- E. Martínez-Moro, On semisimple algebra codes: generator theory, Algebra Discrete Math. 3 (2007), 99–112. Google Scholar
- T. Mora and E. Orsini, Decoding cyclic codes: the Cooper philosophy, this volume, 2009, pp. 69–91. Google Scholar