5 papers
Critical sets of Latin squares based on autoparatopisms
Manuel González-Regadera, Raúl M. Falcón, María Dolores Frau
In cryptography, critical sets of Latin squares have particularly been implemented to design secret sharing schemes. A main problem in these cryptographic protocols arises from abs…
Fundamentals of the cocyclic development of Hadamard matrices over loops
Raúl M. Falcón, Manuel González-Regadera, Félix Gudiel
This paper establishes a formal framework for the cocyclic development of Hadamard matrices over loops based on a novel cohomology theory with associativity obstructions. In this c…
An algebraic approach to Latin squares of prime power order by local permutation polynomials
Raúl M. Falcón, Jaime Gutiérrez, Jorge Jiménez Urroz
Every Latin square of prime power order is uniquely described by a local permutation polynomial (LPP) in the polynomial ring . Despite this equivalence, one…
Heffter arrays over partial loops
Raúl M. Falcón, Lorenzo Mella
A Heffter array over an additive group is any partially filled array satisfying that: (1) each one of its rows and columns sum to zero in , and (2) if $i\in G\setminus\{…
The Hadamard multiary quasigroup product
Raúl M. Falcón, L. Mella, P. Vojtěchovský
The Hadamard quasigroup product has recently been introduced as a natural generalization of the classical Hadamard product of matrices. It is defined as the superposition operator…