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Set systems with restricted symmetric sets of Hamming distances modulo a prime number
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Journal Article
Set systems with restricted symmetric sets of Hamming distances modulo a prime number
2025
Overview
Let
p
be a prime and let
D
=
{
d
1
,
d
2
,
⋯
,
d
s
}
be a subset of
1
,
2
,
⋯
,
p
-
1
.
If
F
is a Hamming symmetric family of subsets of
[
n
]
such that
|
F
△
F
′
|
(
mod
p
)
∈
D
and
n
-
|
F
△
F
′
|
(
mod
p
)
∈
D
for any pair of distinct
F
,
F
′
∈
F
, then
|
F
|
≤
n
-
1
s
+
n
-
1
s
-
1
+
⋯
+
n
-
1
0
.
This result can be considered as a modular version of Hegedüs's Theorem [6] about Hamming symmetric families. We also improve the above upper bound on the size of Hamming symmetric families in the non-modular version when the size of any member of
F
is restricted.
Publisher
Springer International Publishing,Springer Nature B.V
Subject
