Holey Schröder designs of type 4n u1

Existence of HSOLSSOMs of type 4nu1

This paper investigates the existence of holey self-orthogonal Latin squares with a symmetric orthogonal mate of type 4u (briefly HSOLSSOM(4u)). For u > 0, the necessary conditions for existence of such an HSOLSSOM are (1) u must be even, and (2) u ≤ (4n−4)/3, and either (n, u) = (4, 4) or n ≥ 5. We show that these conditions are sufficient except possibly (1) for 36 cases with n ≤ 37, (2) for ...

Resolvable holey group divisible designs with block size three

Signed group orthogonal designs and their applications

Craigen introduced and studied signed group Hadamard matrices extensively in [1, 2]. Livinskyi [13], following Craigen’s lead, studied and provided a better estimate for the asymptotic existence of signed group Hadamard matrices and consequently improved the asymptotic existence of Hadamard matrices. In this paper, we introduce and study signed group orthogonal designs. The main results include...

Holey Schrr Oder Designs of Type 2 N U 1

A holey Schrr oder design of type h n 1 1 h n 2 2 h n k k (HSD(h n 1 1 h n 2 2 h n k k)) is equivalent to a frame idempotent Schrr oder quasigroup (FISQ(h n 1 1 h n 2 2 h n k k)) of order m with n i missing subquasigroups (holes) of order h i ; 1 i k, which are disjoint and spanning, that is , P 1ik n i h i = m. In this paper, we rst consider the existence of HSD(2 n u 1) for 1 u 4 and show tha...

On the Twin Designs with the Ionin-type Parameters

Let 4n2 be the order of a Bush-type Hadamard matrix with q = (2n − 1)2 a prime power. It is shown that there is a weighing matrix W (4(q + qm−1 + · · ·+ q + 1)n, 4qn) which includes two symmetric designs with the Ionin–type parameters ν = 4(q + qm−1 + · · ·+ q + 1)n, κ = q(2n − n), λ = q(n − n) for every positive integer m. Noting that Bush–type Hadamard matrices of order 16n2 exist for all n f...