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We study tight projective 2-designs in three different settings. In the complex setting, Zauners conjecture predicts the existence of a tight projective 2-design in every dimension. Pandey, Paulsen, Prakash, and Rahaman recently proposed an approach to make quantitative progress on this conjecture in terms of the entanglement breaking rank of a certain quantum channel. We show that this quantity is equal to the size of the smallest weighted projective 2-design. Next, in the finite field setting, we introduce a notion of projective 2-designs, we characterize when such projective 2-designs are tight, and we provide a construction of such objects. Finally, in the quaternionic setting, we show that every tight projective 2-design for H^d determines an equi-isoclinic tight fusion frame of d(2d-1) subspaces of R^d(2d+1) of dimension 3.
Consider two sequences of $n$ independent and identically distributed fair coin tosses, $X=(X_1,ldots,X_n)$ and $Y=(Y_1,ldots,Y_n)$, which are $rho$-correlated for each $j$, i.e. $mathbb{P}[X_j=Y_j] = {1+rhoover 2}$. We study the question of how larg
This paper is concerned with the affine-invariant ternary codes which are defined by Hermitian functions. We compute the incidence matrices of 2-designs that are supported by the minimum weight codewords of these ternary codes. The linear codes gener
Projective Reed-Solomon (PRS) codes are Reed-Solomon codes of the maximum possible length q+1. The classification of deep holes --received words with maximum possible error distance-- for PRS codes is an important and difficult problem. In this paper
Tang and Ding [IEEE IT 67 (2021) 244-254] studied the class of narrow-sense BCH codes $mathcal{C}_{(q,q+1,4,1)}$ and their dual codes with $q=2^m$ and established that the codewords of the minimum (or the second minimum) weight in these codes support
This note outlines the steps for proving that the moments of a randomly-selected subset of a general ETF (complex, with aspect ratio $0<gamma<1$) converge to the corresponding MANOVA moments. We bring here an extension for the proof of the Kesten-Mck