On Hadamard full propelinear codes with associated group C_{2t}\times C_2
| Autor: | Ivan Bailera, Josep Rifà, Joaquim Borges |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Rank (linear algebra) Computer Networks and Communications Computer Science::Information Retrieval Applied Mathematics Dimension (graph theory) Order (ring theory) Microbiology Combinatorics Kernel (algebra) Direct product of groups Complex Hadamard matrix Hadamard transform Discrete Mathematics and Combinatorics Circulant matrix Mathematics |
| Zdroj: | Advances in Mathematics of Communications. 15:35-54 |
| ISSN: | 1930-5338 |
| Popis: | We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is \begin{document}$ C_{2t}\times C_2 $\end{document} . We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hadamard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by \begin{document}$ 3 $\end{document} if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order \begin{document}$ 16 $\end{document} . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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