Correction of paper published in J. Combinatorial Theory 21, 1976: On the Existence of Hadamard Matrices

TL;DR

This paper revisits a 1976 study on Hadamard matrices, clarifying the actual bounds for their existence and correcting an error in the original proof.

Contribution

It identifies and corrects an error in the original proof regarding the bounds for constructing Hadamard matrices.

Findings

The original proof's bound was not valid.

A corrected bound for Hadamard matrix construction is provided.

The paper clarifies the conditions for the existence of Hadamard matrices.

Abstract

In the paper On the Existence of Hadamard Matrices in J. Combinatorial Theory 21, 1976, it is shown that for a natural number q > 3, we can construct an Hadamard Matrix of order 2^s q for s \geq t where t = [2 log_2(q-3)]. I will show that this bound is not a consequence of the proof given in the paper and explain the error in the argumentation.