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Symmetric Hadamard matrices of orders 268, 412, 436 and 604

N. A. Balonin, D. Z. Djokovic

TL;DR

This work has constructed, for the first time, symmetric Hadamard matrices of order 268, 412, 436 and 604 by using the so called propus construction for the search of three cyclic blocks to construct Hadamards of propus type.

Abstract

We construct many symmetric Hadamard matrices of small order by using the so called propus construction. The necessary difference families are constructed by restricting the search to the families which admit a nontrivial multiplier. Our main result is that we have constructed, for the first time, symmetric Hadamard matrices of order 268, 412, 436 and 604.

Symmetric Hadamard matrices of orders 268, 412, 436 and 604

TL;DR

This work has constructed, for the first time, symmetric Hadamard matrices of order 268, 412, 436 and 604 by using the so called propus construction for the search of three cyclic blocks to construct Hadamards of propus type.

Abstract

We construct many symmetric Hadamard matrices of small order by using the so called propus construction. The necessary difference families are constructed by restricting the search to the families which admit a nontrivial multiplier. Our main result is that we have constructed, for the first time, symmetric Hadamard matrices of order 268, 412, 436 and 604.

Paper Structure

This paper contains 6 sections, 13 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The cases $v=67,103,109,151$
  4. Some new balanced optimal binary sequences
  5. Propus difference families
  6. Acknowledgements

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Definition 3