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Table 1.
Some possible parameters for our construction and corresponding possible
set sizes for the construction in [8] for
M
=2
,N
= 254
,
and
η
=2(Here
L
∗
denotes
the optimal set size)
Possible set size
in [8]
N
Z
L
L
∗
η
4
6
8
10
12
14
16
18
19
20
22
24
28
30
36
40
50
62
62
40
30
24
20
16
62
64
43
32
25
21
18
16
14
13
12
11
10
9
8
7
6
5
4
30
20
14
14
12
254
2
12
10
10
8
8
6
6
4
4
By Theorem 3, the optimal set size
L
∗
for an (
N, L, Z, η
) LCZ sequence set is
given by
η
2
.
If
N
=2
T
,
Z
=2
d
,and
η
=2
,thenwehave
L
∗
=
1
L
∗
=
1
N
2
η
2
−
Z
·
N
−
(2
T
)
2
−
4
2
2
d
·
2
T
−
4
2
which goes to
d
when
is suciently small compared to
T
. Therefore, the
(2
T,
2
2
T−
1
4
d
,
2
d,
2
)or(2
T,
2
2
T−
3
4
d
,
2
d,
2
) LCZ sequence set
given in
Theorem 2 may be optimal or nearly optimal with respect to the bound in
Theorem 3.
From the construction given in Section III, it is possible to get a (2(2
n
IS
−
1)
,
2
f,
2
d,
2) binary LCZ sequence set by selecting a binary sequence with ideal
autocorrelation as the component sequence
2
n−
1
1and
f
is given in (1). Table 1 compares some possible parameters in our construction
with those by the constructions in [8] when
M
=2,
N
= 254, and
η
=2.
Remark:
Table 1 shows that our construction has an LCZ size greater than or
equal to that of the constructions in [8] for the same set size. Note that there is
no case which has an optimal set size for the constructions in [8]. However, our
construction gives an optimal set size for some cases.
{
s
(
t
)
}
,where2
≤
d
≤
−
