Mutually unbiased maximally entangled bases in $$\mathbb {C}^d\otimes \mathbb {C}^{kd}$$ C d ⊗ C k d

Unextendible maximally entangled bases and mutually unbiased bases

Computing minimal interpolants in $C^{1, 1}(\mathbb{R}^d)$

We consider the following interpolation problem. Suppose one is given a finite set E ⊂ R, a function f : E → R, and possibly the gradients of f at the points of E. We want to interpolate the given information with a function F ∈ C(R) with the minimum possible value of Lip(∇F ). We present practical, efficient algorithms for constructing an F such that Lip(∇F ) is minimal, or for less computatio...

On mutually unbiased bases: Passing from d to d dimensions

We show how to transform the problem of finding d + 1 mutually unbiased bases in Cd into the one of finding d(d+1) vectors in Cd 2 . The transformation formulas admit a solution when d is a prime number.

Frames for subspaces of $\mathbb{C}^N$

We present a theory of finite frames for subspaces of C N. The definition of a subspace frame is given and results analogous to those from frame theory for C N are proven.

$(1-2u^k)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_+u^{3}\mathbb{F}_{p}+\dots+u^{k}\mathbb{F}_{p}$

Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^k)$-constacyclic codes over the ring $\mathcal{R}=\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p+u^{3}\mathbb{F}_{p}+\cdots+u^{k}\mathbb{F}_{p}$ where $u^{k+1}=u$. We illustrate the generator polynomials and investigate the structural properties of these codes via decomposition theorem.