Existence conjecture for Hadamard matrices of 2N-type

A Hadamard matrix of 2N-type is a Hadamard matrix of order 2v2v of the block form

H=[ABBTAT],H=\left[\begin{array}{cc}A&B\\-B^T&A^T\end{array}\right],

where AA and BB are negacyclic blocks. 2N-type existence conjecture. For each even integer v>0v>0, there exists a Hadamard matrix of 2N-type and order 2v2v. Via the bijection between such matrices and NG-pairs, this is equivalent to the assertion that NG-pairs exist for all even lengths; the source gives no general construction and notes the absence of a pair of length 9494.

Sources & referencesView supporting material

Primary source

N. A. Balonin and D. Z. Djokovic, “Negaperiodic Golay pairs and Hadamard matrices”, arXiv:1508.00640 (2015).

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