On the non-existence of maximal difference matrices of deficiency 1

A matrix with entries from a group of order is called a -difference matrix over if the list of quotients contains each element of exactly times for all Jungnickel has shown that and it is conjectured that the equality holds only if is a -group for a prime On the other hand, Winterhof has shown that...

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Bibliographic Details
Published inDesigns, codes, and cryptography Vol. 72; no. 3; pp. 627 - 635
Main Author Hiramine, Yutaka
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.09.2014
Springer
Subjects
Circuits
Coding and Information Theory
Combinatorics
Combinatorics. Ordered structures
Computer Science
Cryptology
Data Structures and Information Theory
Designs and configurations
Discrete Mathematics in Computer Science
Exact sciences and technology
Information and Communication
Mathematics
Sciences and techniques of general use
Difference matrix
Generalized Hadamard matrix
Butson Hadamard matrix
05B20
Hadamard matrix
Abelian group
Quotient
Non existence
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Summary:A matrix with entries from a group of order is called a -difference matrix over if the list of quotients contains each element of exactly times for all Jungnickel has shown that and it is conjectured that the equality holds only if is a -group for a prime On the other hand, Winterhof has shown that some known results on the non-existence of -difference matrices are extended to -difference matrices. This fact suggests us that there is a close connection between these two cases. In this article we show that any -difference matrix over an abelian -group can be extended to a -difference matrix.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-013-9794-7