Balancedly splittable Hadamard matrices
Hadi Kharaghani, Sho Suda
TL;DR
This paper introduces balancedly splittable Hadamard matrices, explores their connections to various combinatorial structures, and presents new construction methods and applications in association schemes.
Contribution
It is the first to define and analyze balancedly splittable Hadamard matrices, linking them to strongly regular graphs, equiangular lines, and unbiased matrices, with new construction techniques.
Findings
Established connections to strongly regular graphs and equiangular lines.
Developed several new construction methods for these matrices.
Constructed new association schemes with 4, 5, and 6 classes.
Abstract
Balancedly splittable Hadamard matrices are introduced and studied. A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased Hadamard matrices. Several construction methods are presented. As an application, commutative association schemes of 4, 5, and 6 classes are constructed.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Finite Group Theory Research