Abstract
AbstractIn this paper the following result is proved. Suppose there exists a C-matrix of order n + 1. Then if n≡1 (mod 4) there exists a Hadamard matrix of order 2nr(n + 1), while if n≡3 (mod 4) there exists a Hadamard matrix of order nr(n + 1) for all r ≧0. If n≡1 (mod 4) is a prime power, the method is adapted to prove the existence of a Hadamard matrix of the Williamson type, of order 2nr(n + 1), for all r ≧0.
Publisher
Cambridge University Press (CUP)
Reference14 articles.
1. Hadamard’s determinant theorem and the sum of four squares
2. Some matrices of Williamson type;Wallis;Utilitas Math.,1973
3. An infinite class of Williamson matrices
4. Spence E. (to appear), “Skew-Hadamard matrices of order 2(q + 1)”, Discrete Math.
5. On Orthogonal Matrices
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. References;Hadamard Matrices;2020-08-06
2. Construction of relative difference sets and Hadamard groups;Designs, Codes and Cryptography;2013-03-24
3. A construction of Hadamard matrices;Journal of Combinatorial Theory, Series A;1991-05
4. On composition of four-symbol -codes and Hadamard matrices;Proceedings of the American Mathematical Society;1989
5. Recurrence formulas for the construction of Williamson-type matrices;Mathematical Notes of the Academy of Sciences of the USSR;1981-10