Construction of Weakly Self-Dual Normal Bases and Its Aplication in Orthogonal Transform Encoding Cyclic Codes
1 Algebra Research Group, Faculty of Mathematic and Natural Sciences, Bandung Institute of Technology
2 Combinatorial Research Group, Faculty of Mathematic and Natural Sciences, Bandung Institute of Technology
Published online: 28 March 2014
In 1986 Fumy proposed a simplified approach to calculate inverse discrete Fourier transform (IDFT) using normal bases and its dual in encoding cyclic codes in the spectral domain. Therefore, one important thing in Fumy’s procedure is to choose an appropriate normal bases such that the dual bases can be determined easily. This problem leads to an application of weakly self-dual normal bases. In this paper we explain how to construct weakly self-dual normal bases and its type of bases in encoding cyclic codes.
Key words: Cyclic codes / Discrete Fourier transform / Inverse discrete Fourier transform / Weakly self-dual normal bases
© Owned by the authors, published by EDP Sciences, 2014
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.