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arXiv · 2506.20778

Asymmetric SICs over finite fields

Joseph W. Iverson·Dustin G. Mixon
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Abstract

Zauner's conjecture concerns the existence of $d^2$ equiangular lines in $\mathbb{C}^d$; such a system of lines is known as a SIC. In this paper, we construct infinitely many new SICs over finite fields. While all previously known SICs exhibit Weyl--Heisenberg symmetry, some of our new SICs exhibit trivial automorphism groups. We conjecture that such \textit{totally asymmetric} SICs exist in infinitely many dimensions in the finite field setting.

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Joseph W. Iverson, Dustin G. Mixon. 2025-06-25. Asymmetric SICs over finite fields. https://arxiv.org/abs/2506.20778

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