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Creators/Authors contains: "Iverson, Joseph W"

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  1. ; (, Information and Inference: A Journal of the IMA)
    Abstract We show the optimal coherence of $2d$ lines in $$\mathbb{C}^{d}$$ is given by the Welch bound whenever a skew Hadamard matrix of order $d+1$ exists. Our proof uses a variant of Hadamard matrix doubling that converts any equiangular tight frame of size $$\tfrac{d-1}{2} \times d$$ into another one of size $$d \times 2d$$. Among $$d \leq 160$$, this produces equiangular tight frames of new sizes when $d = 11$, $35$, $39$, $43$, $47$, $59$, $67$, $71$, $83$, $95$, $103$, $107$, $111$, $119$, $123$, $127$, $131$, $143$, $151$ and $155$. 
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    Free, publicly-accessible full text available March 26, 2026
  2. ; ; (, IEEE Transactions on Information Theory)
    Free, publicly-accessible full text available April 1, 2026
  3. ; ; ; (, Linear Algebra and its Applications)
    Free, publicly-accessible full text available December 1, 2025
  4. ; ; ; (, Designs, Codes and Cryptography)
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  5. ; ; ; (, Finite Fields and Their Applications)
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  6. ; (, Journal of Functional Analysis)
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  7. ; ; (, Forum of Mathematics, Sigma)
    We provide a general program for finding nice arrangements of points in real or complex projective space from transitive actions of finite groups. In many cases, these arrangements are optimal in the sense of maximizing the minimum distance. We introduce our program in terms of general Schurian association schemes before focusing on the special case of Gelfand pairs. Notably, our program unifies a variety of existing packings with heretofore disparate constructions. In addition, we leverage our program to construct the first known infinite family of equiangular lines with Heisenberg symmetry. 
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  8. ; ; (, Journal of Combinatorial Designs)
    Abstract We study tight projective 2‐designs in three different settings. In the complex setting, Zauner's 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 determines an equi‐isoclinic tight fusion frame of subspaces of of dimension 3. 
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