Related papers: On the enumeration of some D-optimal designs
We define a new class of binary matrices by maximizing the peak-sidelobe distances in the aperiodic autocorrelations. These matrices can be used as robust position marks for in-plane spatial alignment. The optimal square matrices of…
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…
Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information…
We study codes with parameters of the ternary Hamming $(n=(3^m-1)/2,3^{n-m},3)$ code, i.e., ternary $1$-perfect codes. The rank of the code is defined to be the dimension of its affine span. We characterize ternary $1$-perfect codes of rank…
We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the run time of these algorithms and consider several related…
For any link and for any modulus $m$ we introduce an equivalence relation on the set of non-trivial m-colorings of the link (an m-coloring has values in Z/mZ). Given a diagram of the link, the equivalence class of a non-trivial m-coloring…
A pure quantum state of N subsystems with d levels each is called k-multipartite maximally entangled state, written k-uniform, if all its reductions to k qudits are maximally mixed. These states form a natural generalization of N-qudits GHZ…
Orthogonal sets of idempotents are used to design sets of unitary matrices, known as constellations, such that the modulus of the determinant of the difference of any two distinct elements is greater than $0$. It is shown that unitary…
We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…
The main aim of this paper is to characterize ideals I in the power series ring R=K[[x1,...,xs]] that are finitely determined up to contact equivalence by proving that this is the case if and only if I is an isolated complete intersection…
In this paper, we construct derived equivalences between matrix subrings. As applications, we calculate the global dimensions and the finitistic dimensions of some matrix subrings. And we show that the finitistic dimension conjecture holds…
We exhibit, for each even degree, a ternary form of rank strictly greater than the maximum rank of monomials. Together with an earlier result in the odd case, this gives the lower bound…
This paper considers how many conjugacy classes of reflections a map can have, under various transitivity conditions. It is shown that for vertex- and for face-transitive maps there is no restriction on their number or size, whereas…
One of the fundamental problem in the theory of sorting is to find the pessimistic number of comparisons sufficient to sort a given number of elements. Currently 16 is the lowest number of elements for which we do not know the exact value.…
Odd, positive-definite, integral, unimodular lattices N of rank 24 were classified by Borcherds. There are 273 isometry classes of such lattices. Associated to them are vertex superalgebras $V_N$ of central charge c=24. We show that at…
A new construction of complex Hadamard matrices of composite order d=pq, with primes p,q, is presented which is based on pairs of mutually unbiased bases containing only product states. For product dimensions d < 100, we illustrate the…
We study the class of finite lattices that are isomorphic to the congruence lattices of algebras from a given finitely generated congruence-distributive variety. If this class is as large as allowed by an obvious necessary condition, the…
It is conjectured that Hadamard matrices exist for all orders $4t$ ($t>0$). However, despite a sustained effort over more than five decades, the strongest overall existence results are asymptotic results of the form: for all odd natural…
A maximal commutative subalgebra is a substructure in algebra with the greatest commutative property. By studying the lengths of maximal commutative subalgebras, one can more clearly characterize the structure of commutative subalgebras in…
Let $q$ be a prime power of the form $q=12c^2+4c+3$ with $c$ an arbitrary integer. In this paper we construct a difference family with parameters $(2q^2;q^2,q^2,q^2,q^2-1;2q^2-2)$ in ${\mathbb Z}_2\times ({\mathbb F}_{q^2},+)$. As a…