Almost Difference Sets, Normally Regular Digraphs and Cyclotomic Schemes from Cyclotomy of Order Twelve

2013/10/04 by Kathleen Nowak, Nowak, Kathleen, Oktay Olmez +5
Computer Science · Engineering · Mathematics · #05B05 #05E30 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05B05 #msc:05E30

paper · pdf · doi:10.48550/arxiv.1310.1164

This paper has been withdrawn by the author due to an error that needs to be fixed

openalex publication_date 2013/10/04 · arxiv created 2013/10/15 · arxiv updated 2013/10/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Using cyclotomic classes of order twelve for certain finite fields, we construct an infinite family of almost difference sets and normally regular graphs applying the theory of cyclotomy. We show that in each of these fields neither the multiplicative cyclic subgroup C of index twelve nor C∪ \0\ forms an almost difference set, but a union of cosets of C provides us an almost difference set. We also calculate the intersection numbers and character tables of cyclotomic association schemes of class two, three and four obtained from these fields.

Related

• Almost Difference Sets from Unions of Cyclotomic Classes of Order 14
• Cyclotomy, difference sets, sequences with low correlation, strongly regular graphs, and related geometric substructures
• Skew Hadamard difference sets from cyclotomic strongly regular graphs
• Cyclotomic Constructions of Skew Hadamard Difference Sets
• The Multiple Equal-Difference Structure of Cyclotomic Cosets