Hadamard partitioned difference families and their descendants
If D is a ( 4 u 2 , 2 u 2 − u , u 2 − u ) Hadamard difference set (HDS) in G , then { G , G ∖ D } is clearly a ( 4 u 2 , [ 2 u 2 − u , 2 u 2 + u ] , 2 u 2 ) partitioned difference family (PDF). Any ( v , K , λ ) -PDF will be said a Hadamard PDF if v = 2 λ as the one above. We present a doubling cons...
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| Veröffentlicht in: | Cryptography and communications 2019-07, Vol.11 (4), p.557-562 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | If
D
is a
(
4
u
2
,
2
u
2
−
u
,
u
2
−
u
)
Hadamard difference set (HDS) in
G
, then
{
G
,
G
∖
D
}
is clearly a
(
4
u
2
,
[
2
u
2
−
u
,
2
u
2
+
u
]
,
2
u
2
)
partitioned difference family (PDF). Any
(
v
,
K
,
λ
)
-PDF will be said a Hadamard PDF if
v
=
2
λ
as the one above. We present a doubling construction which, starting from any Hadamard PDF, leads to an infinite class of PDFs. As a special consequence, we get a PDF in a group of order
4
u
2
(
2
n
+
1
)
and three block-sizes
4
u
2
−
2
u
,
4
u
2
and
4
u
2
+
2
u
, whenever we have a
(
4
u
2
,
2
u
2
−
u
,
u
2
−
u
)
-HDS and the maximal prime power divisors of
2
n
+
1
are all greater than
4
u
2
+
2
u
. |
|---|---|
| ISSN: | 1936-2447 1936-2455 |
| DOI: | 10.1007/s12095-018-0308-3 |