Pseudococyclic Partial Hadamard Matrices over Latin Rectangles

Abstract

The classical design of cocyclic Hadamard matrices has recently been generalized by means of both the notions of the cocycle of Hadamard matrices over Latin rectangles and the pseudococycle of Hadamard matrices over quasigroups. This paper delves into this topic by introducing the concept of the pseudococycle of a partial Hadamard matrix over a Latin rectangle, whose fundamentals are comprehensively studied and illustrated.

Hadamard Matrices with Cocyclic Core

“…It endows the matrix with an enriched structure, which is being successfully exploited to look for Hadamard matrices [2,6,7]. Nowadays, this framework is broadening its expected horizons, since more recently even quasigroups [8] and Latin rectangles [9] have come into play.…”