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Some new symmetric Hadamard matrices

Dragomir Ž. Đoković

Abstract

First examples of symmetric Hadamard matrices of orders 508 and 764 are constructed. The method used is known as the propus construction. A conjecture regarding this method is formally proposed but it appears implicitly in three previous joint papers with N. A. Balonin et alias. The conjecture has been verified for Hadamard matrices of order 4v with odd v<54. In this note the conjecture is verified for v=55,57,59,61,63.

Some new symmetric Hadamard matrices

Abstract

First examples of symmetric Hadamard matrices of orders 508 and 764 are constructed. The method used is known as the propus construction. A conjecture regarding this method is formally proposed but it appears implicitly in three previous joint papers with N. A. Balonin et alias. The conjecture has been verified for Hadamard matrices of order 4v with odd v<54. In this note the conjecture is verified for v=55,57,59,61,63.

Paper Structure

This paper contains 5 sections, 18 equations.

Table of Contents

  1. Introduction
  2. Symmetric Hadamard matrices of orders 508 and 764
  3. Small orders of symmetric Hadamard matrices
  4. List of PPSs and PDFs for odd $v$, $53 < v \le 63$
  5. Acknowledgements

Theorems & Definitions (2)

  • Conjecture 1
  • Example 1