2015/01/27 by Víctor Álvarez, V. Alvarez, Félix Gudiel +11
Computer Science · Engineering · Mathematics · #05B20 #Coding theory and cryptography #Combinatorics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Hadamard matrix #Hadamard transform #Mathematical analysis #Mathematics #Physics #graph theory and CDMA systems #math.CO #msc:05B20
paper · pdf · doi:10.48550/arxiv.1501.06749
12 pages
arxiv created 2015/01/27 · openalex publication_date 2015/01/27 · arxiv updated 2015/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One of the most promising structural approaches to resolving the Hadamard Conjecture uses the family of cocyclic matrices over \mathbb Z t × \mathbb Z22. Two types of equivalence relations for classifying cocyclic matrices over \mathbb Z t × \mathbb Z22 have been found. Any cocyclic matrix equivalent by either of these relations to a Hadamard matrix will also be Hadamard. One type, based on algebraic relations between cocycles over any finite group, has been known for some time. Recently, and independently, a second type, based on four geometric relations between diagrammatic visualisations of cocyclic matrices over \mathbb Z t × \mathbb Z22, has been found. Here we translate the algebraic equivalences to diagrammatic equivalences and show one of the diagrammatic equivalences cannot be obtained this way. This additional equivalence is shown to be the geometric translation of matrix transposition.