Document Type

Article

Publication Date

10-9-2018

Abstract

An equiangular tight frame (ETF) is a type of optimal packing of lines in a real or complex Hilbert space. In the complex case, the existence of an ETF of a given size remains an open problem in many cases. In this paper, we observe that many of the known constructions of ETFs are of one of two types. We further provide a new method for combining a given ETF of one of these two types with an appropriate group divisible design (GDD) in order to produce a larger ETF of the same type. By applying this method to known families of ETFs and GDDs, we obtain several new infinite families of ETFs. The real instances of these ETFs correspond to several new infinite families of strongly regular graphs. Our approach was inspired by a seminal paper of Davis and Jedwab which both unified and generalized McFarland and Spence difference sets. We provide combinatorial analogs of their algebraic results, unifying Steiner ETFs with hyperoval ETFs and Tremain ETFs.

Comments

Sourced from the e-print at arXiv:1803.07468v1, https://arxiv.org/abs/1803.7468
Date of arXiv submission: 20 Mar 2018. 12-month embargo passed after October 2019.

Publisher version of record at SpringerLink (subscriber access): https://doi.org/10.1007/s10623-018-0569-z

Publication date refers to the publisher version of record digital edition.

DOI

10.1007/s10623-018-0569-z

Source Publication

Designs, Codes and Cryptography

Included in

Mathematics Commons

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