𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Qualified residue difference sets with zero

✍ Scribed by Derek Jennings; Kevin Byard

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
230 KB
Volume
181
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

We previously established that biquadratic qualified residue difference sets exist for primes p if and only if p = 16x 2 + 1 and sextic qualified residue difference sets exist if and only if p = 108x 2 Γ· 1. For example such sets exist for the primes 17 and 109, respectively. In this paper we point out that if zero is counted as a residue then we can obtain further qualified residue difference sets for both the biquadratic and the sextic residues. We give two theorems which state precisely when such biquadratic and sextic residue sets exist and a further existence theorem for more general powers.

πŸ“œ SIMILAR VOLUMES

An extension for residue difference sets
An extension for residue difference sets
✍ Derek Jennings; Kevin Byard πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 219 KB

In this paper we extend the idea of residue difference sets, with existence theorems being established for certain classes of primes.

Splines with maximal zero sets
Splines with maximal zero sets
✍ Avraham A Melkman πŸ“‚ Article πŸ“… 1977 πŸ› Elsevier Science 🌐 English βš– 708 KB
Relative difference sets with n = 2
Relative difference sets with n = 2
✍ K.T. Arasu; Dieter Jungnickel; Siu Lun Ma; Alexander Pott πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 866 KB

We investigate the existence of relative (m, 2, k, 2)-difference sets in a group H x N relative to N. One can think of these as 'liftings' or 'extensions' of (m, k, 22)-difference sets. We have to distinguish between the difference sets and their complements.. In particular, we prove: --Difference

Cyclic Relative Difference Sets with Cla
Cyclic Relative Difference Sets with Classical Parameters
✍ K.T. Arasu; J.F. Dillon; Ka Hin Leung; Siu Lun Ma πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 121 KB

We investigate the existence of cyclic relative difference sets with parameters ((q d &1)Γ‚(q&1), n, q d&1 , q d&2 (q&1)Γ‚n), q any prime power. One can think of these as ``liftings'' or ``extensions'' of the complements of Singer difference sets. When q is odd or d is even, we find that relative diff