Hadamard matrices: skew of orders 276, 292 and symmetric 372
Dragomir \v{Z}. Djokovi\'c
TL;DR
This paper presents new constructions of skew-Hadamard matrices of orders 276 and 292, and symmetric Hadamard matrices of order 372, advancing the understanding of their existence for specific orders.
Contribution
It introduces novel methods to construct skew-Hadamard matrices of previously unknown orders and provides the first known examples of certain symmetric Hadamard matrices.
Findings
Constructed skew-Hadamard matrices of order 276 and 292
Produced symmetric Hadamard matrices of order 372
Extended the known existence range of these matrices
Abstract
The smallest integer v>0 for which no skew-Hadamard matrix of order 4v is known is v=69. We show how to construct several such matrices. We also construct presumably the first example of a skew-Hadamard matrix of order 292, and the first examples of symmetric Hadamard matrices of order 372.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Mathematics and Applications