Loading…
Bent partitions
Spread and partial spread constructions are the most powerful bent function constructions. A large variety of bent functions from a 2 m -dimensional vector space V 2 m ( p ) over F p into F p can be generated, which are constant on the sets of a partition of V 2 m ( p ) obtained with the subspaces o...
Saved in:
| Published in: | Designs, codes, and cryptography codes, and cryptography, 2022, Vol.90 (4), p.1081-1101 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Spread and partial spread constructions are the most powerful bent function constructions. A large variety of bent functions from a 2
m
-dimensional vector space
V
2
m
(
p
)
over
F
p
into
F
p
can be generated, which are constant on the sets of a partition of
V
2
m
(
p
)
obtained with the subspaces of the (partial) spread. Moreover, from spreads one obtains not only bent functions between elementary abelian groups, but bent functions from
V
2
m
(
p
)
to
B
, where
B
can be any abelian group of order
p
k
,
k
≤
m
. As recently shown (Meidl, Pirsic 2021), partitions from spreads are not the only partitions of
V
2
m
(
2
)
, with these remarkable properties. In this article we present first such partitions—other than (partial) spreads—which we call bent partitions, for
V
2
m
(
p
)
,
p
odd. We investigate general properties of bent partitions, like number and cardinality of the subsets of the partition. We show that with bent partitions we can construct bent functions from
V
2
m
(
p
)
into a cyclic group
Z
p
k
. With these results, we obtain the first constructions of bent functions from
V
2
m
(
p
)
into
Z
p
k
,
p
odd, which provably do not come from (partial) spreads. |
|---|---|
| ISSN: | 0925-1022 1573-7586 |
| DOI: | 10.1007/s10623-022-01029-z |