Corollary 7.8.
Assuming that:
G
=
𝔽
2
n
and
X
1
,
X
2
,
X
3
,
X
4
are independent
G
-valued random variables
Then
d
[
(
X
1
,
X
2
)
;
(
X
3
,
X
4
)
]
=
d
[
X
1
;
X
3
]
+
d
[
X
2
;
X
4
]
=
d
[
X
1
+
X
2
;
X
3
+
X
4
]
+
d
[
X
1
|
X
1
+
X
2
;
X
3
|
X
3
+
X
4
]
+
I
[
X
1
+
X
3
,
X
2
+
X
4
:
X
1
+
X
2
,
X
3
+
X
4
|
X
1
+
X
2
+
X
3
+
X
4
]
⏟
(
∗
)