2022/10/31 by D. V. Zinoviev, Zinoviev, Dmitrii, Victor Zinoviev +1
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2211.00160
openalex publication_date 2022/10/31 · openalex created_date 2022/11/07 · openalex updated_date 2026/07/28
Using the ideas of concatenation construction of codes over the q-ary alphabet, we modify the known generalized Sylvester-type construction of the Hadamard matrices. The new construction is based on two collections of the Hadamard matrices. In particular this construction involves m Hadamard matrices of order k and k Hadamard matrices of order m. These matrices are not necessary different. As a result we obtain a Hadamard matrix of order km. The new construction gives many possibilities for construction of the new Hadamard matrices with different ranks and dimension of kernel.