Type of the equiangular tight frames with \(n+1\) vectors in \(R^n\)

Abstract

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An equiangular tight frame (ETF) is a \(d \times n\) matrix that has orthogonal rows and unit-norm columns. ETFs have applications in communications, coding theory and quantum computing. In this paper we investigate type of ETFs that have \(n+1\) vectors in \(R^n\). Also we state the connection between these frames with the complete graphs that containing \(n+1\) vertices.