Information Technology Reference
In-Depth Information
))) and row(
t
(
z
i
))
>
mid(row(
t
(
(i) row(
t
(
y
i
))
<
mid(row(
t
(
x
x
)))
,
))) and row(
t
(
z
i
))
<
mid(row(
t
(
(ii) row(
t
(
y
i
))
>
mid(row(
t
(
x
x
)))
.
ʵ
f
s
(
y
3
)
s
0
(
z
3
)
t
(
y
3
)
t
(
z
3
)
M
ʵ
f
s
(
y
2
)
t
(
y
2
)
t
(
z
2
)
s
0
(
z
2
)
M
f
t
(
y
1
)
t
(
z
1
)
s
(
y
1
)
s
0
(
z
1
)
M
:= mid(row(
t
(
x
)))
M
:= mid(row(
t
(
x
)))
s
=
h
(
f ⓦ t
)
s
0
:=
h
(
f ⓦ t
)
Fig. 2
Since
|I|≤k −
1, choosing
a
:= (
f ⓦt
(
z
i
))
i∈I
we find by item 4 of Theorem
8 an automorphism
f
a
that swaps
f
t
(
z
i
)to
ʵ
t
(
z
i
), for each
i
ⓦ
ⓦ
f
ⓦ
∈
I
, but
t
(
z
i
)))
i∈I
fixed.
leaves all elements in rows of distance
>
1 from (row(
f
ⓦ
We now let
s
:=
h
(
f
a
ⓦ
t
). Since
f
ⓦ
)))
,
mid(row(
t
(
1
<
mid(row(
t
(
x
x
)))
<n
by the definition, we have 2
<
row(
t
(
z
i
))
<n
−
1, for
i
∈
I
. Hence
f
a
∈F
and
s
∈
Y
∗
.Moreover,for
i
∈
I
, we obtain that
t
(
z
i
)=
ʵ
t
(
z
i
)=
s
(
z
i
)
,
or
(i)
s
(
y
i
)=
f
ⓦ
t
(
y
i
)=
f
ⓦ
ⓦ
f
a
ⓦ
f
ⓦ
t
(
z
i
)=
f
a
ⓦ
t
(
z
i
)=
s
(
z
i
)
.
(ii)
s
(
y
i
)=
ʵ
ⓦ
f
ⓦ
t
(
y
i
)=
ʵ
ⓦ
f
ⓦ
f
ⓦ
