A survey on modular Hadamard matrices Original Research Article

We provide constructions of 32-modular Hadamard matrices for every size n divisible by 4. They are based on the description of several families of modular Golay pairs and quadruples. Higher moduli are also considered, such as image and 192. Finally, we exhibit infinite families of circulant modular Hadamard matrices of various types for suitable moduli and sizes.