In this paper, a new family of relative difference sets with parameters (m, n, k, λ) = ((q − 1)/(q − 1), 4(q− 1), q, q/4) is constructed where q is a 2-power. The construction is based on the technique used in [2]. By a similar method, we also construct some new circulant weighing matrices of order q where q is a 2-power, d is odd and d ≥ 5. Correspondence: S.L. Ma Department of Mathematics Nat...

In this talk we expose the results about infinite families of vertex critical r-dichromatic circulant tournaments for all r ≥ 3. The existence of these infinite families was conjectured by Neumann-Lara [6], who later proved it for all r ≥ 3 and r = 7. Using different methods we find explicit constructions of these infinite families for all r ≥ 3, including the case when r = 7, which complete th...

In this paper we exhibit infinite families of vertex critical r-dichromatic circulant tournaments for all r ≥ 3. The existence of these infinite families was conjectured by NeumannLara (7), who later proved it for all r ≥ 3 and r 6= 7. Using different methods we find explicit constructions of these infinite families for all r ≥ 3, including the case when r = 7, which complets the proof of the c...

We present a way to physically realize a circulant 2-qubit entangling gate in the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4. Our approach uses qubit and qutrit ancillas, braids, fusions and interferometric measurements. Our qubit is formed by four anyons of topological charges 1221. Among other 2qubit entangling gates we generate in the present work, we produce in particula...

A classification of all extremal double circulant self-dual codes of lengths up to 72 is known. In this paper, we give a classification of all extremal double circulant self-dual codes of lengths 74–88. © 2006 Elsevier B.V. All rights reserved.

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order n— i.e., to characterize entire functions f with the property that f(A) is entrywise nonnegative for every entrywise nonnegative matrix A of size n×n. Towards this goal, we present a complete characterization of functions preserving nonnegativity of (block) uppertriangular matri...

In this paper we completely classify the circulant weighing matrices of weight 16 and odd order. It turns out that the order must be an odd multiple of either 21 or 31. Up to equivalence, there are two distinct matrices in CW (31, 16), one matrix in CW (21, 16) and another one in CW (63, 16) (not obtainable by Kronecker product from CW (21, 16)). The classification uses a multiplier existence t...

We disprove the following conjecture due to Vı́ctor Neumann-Lara: for every pair (r, s) of integers such that r > s > 2, there is an infinite set of circulant tournaments T such that the dichromatic number and the cyclic triangle free disconnection of T are equal to r and s, respectively. Let Fr,s denote the set of circulant tournaments T with dc(T ) = r and − →ω 3 (T ) = s. We show that for eve...