๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Supplementary difference sets and Jacobi sums

โœ Scribed by Mieko Yamada

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
752 KB
Volume
103
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis

Yamada, M., Supplementary difference sets and Jacobi sums, Discrete Mathematics 103 (1992) 75-90. Let 4 = ef + 1 be an odd prime power and C,, 1 =Z i =S e -1, be cyclotomic classes of the eth power residues in F = GF(q). Let Ai with #A, = ujr 1 =~i Sn, be non-empty subsets of Q={O,l,..., e-l}andletD,=U,,,, C,, 1s i s n. Here we prove that D,, . . , D,, become n -{q:uJ, ulf, . , uf; A} supplementary difference sets if and only if the following equations are satisfied: (i) ,& ui(uif -1) = 0 (mod e),

(ii) CfcI CkZO n(x", x?)w~,~o~,~_~ = 0, for all t, 1 s t s e -1, where n(xm, x-') is the Jacobi sum for the eth power residue characters and We,,, = ClcAi c;'", where 5', is a primitive eth root of unity. Furthermore, we give numerical results for e = 2, n = 1, 2 and for e = 4, n = 1, 2, 3, 4.

๐Ÿ“œ SIMILAR VOLUMES

Gauss Sums, Jacobi Sums, and p-Ranks of
Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets
โœ Ronald Evans; Henk D.L. Hollmann; Christian Krattenthaler; Qing Xiang ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 301 KB

We study quadratic residue difference sets, GMW difference sets, and difference sets arising from monomial hyperovals, all of which are (2 d &1, 2 d&1 &1, 2 d&2 &1) cyclic difference sets in the multiplicative group of the finite field F 2 d of 2 d elements, with d 2. We show that, except for a few

On supplementary difference sets
On supplementary difference sets
โœ Jennifer Wallis ๐Ÿ“‚ Article ๐Ÿ“… 1972 ๐Ÿ› Springer ๐ŸŒ English โš– 618 KB
Supplementary difference sets and optima
Supplementary difference sets and optimal designs
โœ Christos Koukouvinos; Stratis Kounias; Jennifer Seberry ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 534 KB

## Koukouvinos, C., S. Kounias and J. Seberry, Supplementary difference sets and optimal designs, Discrete Mathematics 49-58. D-optimal designs of order n = 2v -2 (mod 4), where q is a prime power and v = q2 + q + 1 are constructed using two methods, one with supplementary difference sets and the

Optimal designs, supplementary differenc
Optimal designs, supplementary difference sets and multipliers
โœ C. Koukouvinos; Jennifer Seberry; A.L. Whiteman; Ming-yuan Xia ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 327 KB

We investigate multipliers of 2-{v; q2,q2; )~} supplementary difference sets where cyclotomy has been used to construct D-optimal designs.