2018/09/14 by Ka Hin Leung, Leung, Ka Hin, Koji Momihara +1
Engineering · Computer Science · #graph theory and CDMA systems #Coding theory and cryptography
paper · pdf · doi:10.48550/arxiv.1809.05253
In this paper, we obtain a number of new infinite families of Hadamard matrices. Our constructions are based on four new constructions of difference families with four or eight blocks. By applying the Wallis-Whiteman array or the Kharaghani array to the difference families constructed, we obtain new Hadamard matrices of order 4(uv+1) for u=2 and v∈ Φ1∪ Φ2 ∪ Φ3 ∪ Φ4; and for u∈ \3,5\ and v∈ Φ1∪ Φ2 ∪ Φ3. Here, Φ1=\q2:q≡ 1\pmod4 is a prime power\, Φ2=\n4∈ ℕ:n≡ 1\pmod2\ ∪ \9n4∈ ℕ:n≡ 1\pmod2\, Φ3=\5\ and Φ4=\13,37\. Moreover, our construction also yields new Hadamard matrices of order 8(uv+1) for any u∈ Φ1∪ Φ2 and v∈ Φ1∪ Φ2 ∪ Φ3.