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1239
1232
J
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A new
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BCH
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a
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Evaluation Warning : The document was created with Spire.PDF for Python.
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r
B
C
H
co
d
es.
T
h
e
Sectio
n
4
p
r
esen
ts
th
e
m
a
in
r
esu
lt
s
.
T
h
e
co
n
clu
s
io
n
an
d
t
h
e
p
o
s
s
ib
le
f
u
t
u
r
e
d
ir
ec
tio
n
s
o
f
th
is
r
esear
c
h
ar
e
o
u
tli
n
ed
in
S
ec
tio
n
5.
2.
RE
L
AT
E
D
WO
RK
S
T
h
e
d
eter
m
i
n
atio
n
o
f
t
h
e
m
i
n
i
m
u
m
d
is
tan
ce
f
o
r
p
r
i
m
iti
v
e
B
C
H
co
d
es
is
h
ar
d
as
p
o
in
t
ed
o
u
t
b
y
ch
ar
p
in
in
[
1
1
]
.
Fo
r
th
is
r
ea
s
o
n
,
m
a
n
y
r
esear
ch
er
s
h
av
e
i
n
v
esti
g
a
ted
s
ev
er
al
m
et
h
o
d
s
f
o
r
f
i
n
d
in
g
th
i
s
m
etr
ic
.
T
h
is
Sectio
n
s
u
m
m
ar
izes t
h
e
m
o
s
t i
m
p
o
r
tan
t o
n
e
s
.
I
n
[
1
2
]
,
Au
g
o
t,
C
h
ar
p
in
,
a
n
d
Sen
d
r
ier
p
r
esen
ted
an
alg
eb
r
aic
s
y
s
te
m
o
f
Ne
w
to
n
’
s
id
en
titi
e
s
.
T
h
e
ex
is
te
n
ce
of
a
s
o
lu
t
io
n
f
o
r
th
is
s
y
s
te
m
,
p
r
o
v
e
t
h
e
ex
is
te
n
ce
o
f
w
o
r
d
s
o
f
a
g
iv
e
n
w
ei
g
h
t
in
a
co
d
e.
T
h
e
u
s
e
o
f
th
is
m
et
h
o
d
f
o
r
b
o
th
r
em
ai
n
in
g
u
n
k
n
o
w
n
m
i
n
i
m
u
m
d
is
tan
ce
B
C
H
co
d
es
o
f
len
g
th
2
5
5
p
r
o
v
e
th
at
B
C
H(
2
5
5
,
6
3
,
6
1
)
h
as
m
in
i
m
u
m
d
i
s
ta
n
ce
6
3
,
an
d
B
C
H(
2
5
5
,
7
1
,
5
9
)
,
h
as
m
i
n
i
m
u
m
d
is
tan
ce
6
1
.
T
h
e
u
s
e
o
f
th
i
s
m
et
h
o
d
h
ad
y
ield
also
to
n
e
w
r
esu
lt
s
f
o
r
s
o
m
e
B
C
H
co
d
es o
f
len
g
t
h
5
1
1
.
I
n
[
1
3
]
,
C
h
ab
a
u
d
m
ad
e
a
co
m
p
ar
i
s
o
n
o
f
th
e
b
o
th
p
r
o
b
ab
ilis
tic
alg
o
r
it
h
m
s
f
o
r
f
i
n
d
in
g
m
i
n
i
m
u
m
-
w
ei
g
h
t
w
o
r
d
s
in
a
li
n
ea
r
co
d
e
L
eo
n
's
[
1
4
]
an
d
Ster
n
’
s
[
1
5
]
.
Af
ter
th
at,
C
h
ab
a
u
d
w
ith
C
a
n
teau
t
in
[
1
6
]
,
h
av
e
d
ev
elo
p
ed
a
n
e
w
p
r
o
b
ab
ilis
tic
alg
o
r
it
h
m
b
ased
o
n
t
h
e
b
es
t
o
n
e.
T
h
e
ap
p
licatio
n
o
f
t
h
is
alg
o
r
ith
m
o
n
n
ar
r
o
w
-
s
en
s
e
B
C
H
C
o
d
es
o
f
le
n
g
t
h
5
1
1
h
ad
y
ield
to
s
o
m
e
n
e
w
r
esu
lt
s
,
h
o
w
e
v
er
th
e
m
i
n
i
m
u
m
d
is
t
a
n
ce
is
s
till
u
n
k
n
o
w
n
f
o
r
o
th
er
co
d
es.
Z
i
m
m
er
m
a
n
n
alg
o
r
it
h
m
[
1
7
]
is
a
g
e
n
er
al
alg
o
r
it
h
m
f
o
r
co
m
p
u
tin
g
t
h
e
m
in
i
m
u
m
d
is
ta
n
ce
o
f
a
lin
ea
r
co
d
e.
I
t
is
im
p
le
m
e
n
ted
in
G
A
P
(
p
ac
k
ag
e
G
u
av
a)
[
1
8
]
o
v
er
f
ield
s
F
2
an
d
F
3
.
I
t
is
als
o
im
p
le
m
e
n
ted
,
in
Ma
g
m
a
o
v
er
an
y
f
i
n
i
te
f
ield
.
Z
i
m
m
er
m
a
n
n
’
s
al
g
o
r
ith
m
is
e
x
p
lain
ed
in
d
etail
i
n
[
1
9
]
.
W
allis
an
d
Ho
u
g
h
te
n
i
n
[
2
0
]
h
av
e
i
m
p
le
m
e
n
ted
t
h
e
g
e
n
etic
alg
o
r
ith
m
f
o
r
co
m
p
u
ti
n
g
th
e
m
i
n
i
m
u
m
d
is
tan
ce
f
o
r
B
C
H
co
d
es.
Sim
u
latio
n
s
r
esu
lts
s
h
o
w
t
h
at
t
h
e
g
e
n
etic
al
g
o
r
ith
m
o
u
tp
er
f
o
r
m
s
o
th
er
ar
tific
ial
in
telli
g
e
n
ce
tech
n
iq
u
e
s
lik
e
t
h
e
T
ab
u
Sear
ch
p
r
esen
ted
in
[
2
1
]
an
d
h
ill
-
cl
i
m
b
i
n
g
.
I
n
[
2
2
]
,
th
e
au
th
o
r
s
h
a
v
e
o
p
tim
ized
th
e
p
ar
a
m
eter
s
o
f
th
e
g
en
etic
al
g
o
r
ith
m
a
n
d
co
n
s
eq
u
en
t
l
y
t
h
e
y
o
b
tai
n
ed
m
o
r
e
ac
cu
r
ate
r
esu
l
ts
.
B
y
f
o
r
m
u
lati
n
g
an
t
co
lo
n
y
o
p
ti
m
izatio
n
(
AC
O)
to
in
co
r
p
o
r
ate
T
ab
u
Sear
ch
(
T
S),
B
la
n
d
in
[
2
3
]
,
co
n
tin
u
es
to
i
m
p
r
o
v
e
h
is
tab
u
s
ea
r
ch
tech
n
iq
u
e
p
r
ese
n
ted
in
[
2
1
]
.
T
h
is
h
y
b
r
id
tech
n
iq
u
e,
c
alled
A
C
OT
S,
h
ad
y
ield
to
m
o
r
e
ac
cu
r
ate
r
esu
lts
.
T
h
e
ar
tif
icial
i
n
tel
lig
e
n
ce
Si
m
u
lated
An
n
ea
lin
g
p
r
ese
n
ted
i
n
[
2
4
]
w
as
s
h
o
w
n
to
b
e
u
s
e
f
u
l
in
f
i
n
d
in
g
th
e
m
i
n
i
m
u
m
d
is
ta
n
ce
f
o
r
li
n
ea
r
co
d
es.
I
n
[
2
5
]
,
A
j
ith
a
h
as
u
s
ed
th
e
m
etr
o
p
o
lis
alg
o
r
ith
m
to
attac
k
t
h
e
m
i
n
i
m
u
m
w
ei
g
h
t
co
d
e
w
o
r
d
p
r
o
b
lem
.
T
h
is
clo
s
e
al
g
o
r
ith
m
to
th
e
Si
m
u
lated
A
n
n
ea
li
n
g
g
iv
es
m
o
r
e
ac
cu
r
ate
r
esu
lt
s
in
co
m
p
ar
i
s
o
n
to
p
r
ev
io
u
s
w
o
r
k
s
p
r
ese
n
ted
in
[
2
0
]
-
[
2
4
]
.
I
n
[
2
5
]
,
Ay
laj
an
d
B
elk
as
m
i
co
n
tin
u
e
to
i
m
p
r
o
v
et
h
e
Si
m
u
lated
A
n
n
ea
l
in
g
p
r
esen
ted
i
n
[
2
4
]
.
T
h
e
p
r
o
p
o
s
ed
Si
m
u
lated
A
n
n
ea
li
n
g
(
P
SA
)
h
ad
y
ield
to
a
f
ast
co
n
v
er
g
e
n
ce
b
y
r
ed
u
c
in
g
th
e
n
u
m
b
er
o
f
iter
atio
n
s
o
f
th
e
class
ical
Si
m
u
lated
An
n
ea
l
i
n
g
ap
p
r
o
ac
h
as
w
ell
as
o
b
tain
in
g
g
o
o
d
r
esu
lts
i
n
co
m
p
ar
i
s
o
n
t
o
th
e
p
r
ev
io
u
s
w
o
r
k
s
p
r
esen
ted
in
[
2
0
]
,
[
2
2
]
,
[
2
2
]
,
[
2
5
]
.
I
n
[
2
7
]
,
B
er
r
o
u
h
as
p
r
esen
ted
an
ef
f
icie
n
t
ap
p
r
o
ac
h
b
ased
o
n
th
e
n
o
tio
n
o
f
E
r
r
o
r
I
m
p
u
l
s
e
r
esp
o
n
s
e
o
f
a
So
f
t
-
I
n
d
ec
o
d
er
.
T
h
e
p
r
o
p
o
s
ed
id
ea
m
ak
e
a
r
elatio
n
b
et
w
e
en
th
e
m
in
i
m
u
m
d
i
s
tan
ce
a
n
d
th
e
lev
el
o
f
n
o
i
s
e
ad
d
ed
t
o
all
-
ze
r
o
co
d
ew
o
r
d
b
y
co
n
s
id
er
in
g
t
h
e
m
i
n
i
m
u
m
d
is
tan
ce
as
t
h
e
s
m
alle
s
t
lev
el
o
f
n
o
is
e
f
r
o
m
w
h
ich
th
e
d
ec
o
d
er
f
ails
in
co
r
r
ec
tio
n
.
I
n
[
2
2
]
,
th
e
au
th
o
r
s
h
a
v
e
i
m
p
r
o
v
ed
th
i
s
id
ea
an
d
p
r
esen
ted
th
e
M
u
ltip
le
I
m
p
u
l
s
e
Me
th
o
d
(
MI
M)
.
I
n
[
2
8
]
,
th
e
au
t
h
o
r
s
p
r
esen
ted
an
e
f
f
icien
t
lo
ca
l
s
ea
r
ch
tech
n
iq
u
e
ca
lled
MI
M
-
R
SC
,
w
h
ic
h
co
n
s
is
t
i
n
ap
p
l
y
in
g
t
h
e
MI
M
m
eth
o
d
o
n
s
o
m
e
R
an
d
o
m
S
u
b
C
o
d
es
o
f
r
e
d
u
ce
d
d
i
m
en
s
io
n
s
.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
h
ad
y
ie
l
d
to
g
o
o
d
r
esu
lts
co
m
p
ar
ed
to
th
e
p
r
ev
io
u
s
w
o
r
k
s
p
r
esen
ted
in
[
2
0
]
,
[
2
2
]
,
[
2
3
]
,
[
2
5
]
,
[
2
6
]
as
w
ell
as
f
i
n
d
in
g
th
e
tr
u
e
m
i
n
i
m
u
m
d
is
tan
ce
o
f
s
o
m
e
B
C
H
co
d
es o
f
le
n
g
t
h
1
0
2
3
an
d
2
0
4
7
.
3.
T
H
E
P
RO
P
O
SE
D
SCH
E
M
E
I
n
s
tead
o
f
s
ea
r
ch
i
n
g
i
n
s
o
m
e
r
an
d
o
m
s
u
b
co
d
es
li
k
e
i
n
[
2
8
]
,
o
u
r
p
r
o
p
o
s
ed
s
ch
e
m
e
c
o
n
s
is
ts
i
n
s
ea
r
ch
i
n
g
i
n
f
e
w
d
eter
m
in
ed
s
u
b
co
d
es
f
ix
ed
b
y
s
p
ec
ial
p
er
m
u
tatio
n
s
f
r
o
m
t
h
e
au
to
m
o
r
p
h
is
m
g
r
o
u
p
o
f
B
C
H
co
d
es.
I
t
is
w
ell
k
n
o
w
n
th
a
t
f
o
r
B
C
H(
n
=2
m
-
1
,
δ)
co
d
es,
th
e
m
u
ltip
lier
p
er
m
u
tat
io
n
s
d
ef
i
n
ed
o
n
{0
,
1
,
.
.
.
,
n
−1
}
b
y
k
2
μ
:
i→2
k
i
(
m
o
d
n
)
w
it
h
1
≤
k
≤
m
-
1
ar
e
s
tab
ilizer
s
.
Fro
m
th
ese
s
tab
ilizer
s
,
w
e
ta
k
e
o
n
l
y
s
tab
ilizer
s
w
it
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il 2
0
1
9
:
1
2
3
2
-
1239
1234
d
if
f
er
e
n
t
c
y
cle
s
tr
u
ct
u
r
e
b
ec
a
u
s
e
th
e
y
f
i
x
d
i
f
f
er
e
n
t
s
u
b
co
d
e
an
d
ap
p
l
y
Z
i
m
m
er
m
an
n
al
g
o
r
ith
m
o
n
t
h
ese
s
u
b
co
d
es.
Fo
r
f
in
d
i
n
g
t
h
e
m
in
i
m
u
m
d
is
ta
n
ce
o
f
B
C
H
co
d
es.
T
h
e
p
r
o
p
o
s
ed
s
ch
e
m
e
w
o
r
k
s
a
s
f
o
llo
w
s
:
In
p
u
ts:
-
A
g
e
n
e
ra
to
r
m
a
tri
x
G
o
f
BCH
(n
=
2
m
-
1
,
k
,
δ
)
-
T
h
e
p
e
rm
u
tatio
n
s
j
i
2
μ
1
≤i≤N
w
it
h
d
iff
e
re
n
t
c
y
c
le stru
c
tu
re
S
tep
1
:
F
o
r
k
=
1
t
o
N d
o
F
in
d
th
e
s
u
b
c
o
d
e
f
ix
e
d
b
y
j
k
2
μ
En
d
f
o
r
S
tep
2
:
F
o
r
k
=
1
t
o
N d
o
F
in
d
th
e
e
stim
a
ted
m
in
i
m
u
m
d
istan
c
e
d
o
f
th
e
su
b
c
o
d
e
f
ix
e
d
b
y
j
k
2
μ
b
y
u
sin
g
th
e
Zi
m
m
e
r
m
a
n
n
a
lg
o
rit
h
m
.
En
d
f
o
r
Ou
tp
u
t:
-
d
a
s es
ti
m
a
ted
m
in
i
m
u
m
d
istan
c
e
o
f
BCH(n
,
k
,
δ
)
E
x
a
m
p
le
s
:
L
et’
s
ta
k
e
th
eB
C
H
(
1
5
,
5
,
7
)
c
o
d
e.
A
s
y
s
te
m
at
ic
g
e
n
er
ato
r
m
atr
ix
o
f
B
C
H(
1
5
,
5
,
7
)
co
d
e
is
:
1 0 0 0 0
1 1 1 0 1
1 0 0 1 0
0 1 0 0 0
0 1 1 1 0
1 1 0 0 1
0 0 1 0 0
1 1 0 1 0
1 1 1 1 0
0 0 0 1 0
0 1 1 0 1
0 1 1 1 1
0 0 0 0 1
1 1 0 1 1
0 0 1 0 1
G
B
y
u
s
i
n
g
a
m
ath
e
m
at
ical
to
o
l,
w
e
o
b
tai
n
t
h
e
g
e
n
er
ato
r
m
atr
i
x
GS1
o
f
t
h
e
s
u
b
co
d
e
f
i
x
ed
b
y
µ
2
=(
0
)
(
1
,
2
,
4
,
8
)
(
3
,
6
,
1
2
,
9
)
(
5
,
1
0
)
(
7
,
1
4
,
1
3
,
1
1
)
an
d
th
e
g
e
n
er
ato
r
m
atr
ix
GS2
o
f
t
h
e
s
u
b
co
d
e
f
ix
ed
b
y
µ
4
=(
0
)
(
1
,
4
)
(
2
,
8
)
(
3
,
1
2
)
(
6
,
9
)
(
5
)
(
1
0
)
(
7
,
1
3
)
(
1
4
,
1
1
)
:
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
GS
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
GS
I
n
th
e
s
ec
o
n
d
s
tep
,
b
y
ap
p
l
y
i
n
g
th
e
Z
i
m
m
er
m
a
n
n
al
g
o
r
i
th
m
o
n
t
h
e
f
ir
s
t
s
u
b
co
d
e,
th
e
m
i
n
i
m
u
m
d
is
tan
ce
o
b
tain
ed
is
eq
u
al
to
7
,
w
h
ich
i
s
t
h
e
d
esig
n
ed
d
is
ta
n
c
e
f
o
r
th
e
co
n
s
id
er
ed
B
C
H
co
d
e,
an
d
th
er
ef
o
r
e
th
e
m
i
n
i
m
u
m
d
is
ta
n
ce
is
7
.
L
et
’
s
n
o
w
ta
k
e
a
n
o
th
er
e
x
a
m
p
le
o
f
th
e
B
C
H(
5
1
1
,
3
5
8
,
3
7
)
co
d
e.
T
h
e
p
er
m
u
tatio
n
s
μ
2
,
μ
4
,
μ
16
,
μ
32
,
μ
128
,
an
d
μ
256
h
a
v
e
t
h
e
s
a
m
e
c
y
cle
s
tr
u
ct
u
r
e
a
n
d
f
i
x
t
h
e
s
a
m
e
s
u
b
co
d
e.
O
n
t
h
e
o
th
er
h
a
n
d
,
th
e
p
er
m
u
tatio
n
s
μ
8
an
d
μ
64
f
i
x
al
s
o
th
e
s
a
m
e
s
u
b
co
d
e.
B
y
u
s
i
n
g
a
m
a
th
e
m
atica
l
to
o
l,
w
e
o
b
tai
n
t
h
e
g
e
n
er
ato
r
s
m
a
tr
ix
o
f
t
h
e
s
u
b
co
d
e
f
ix
ed
b
y
μ
2
an
d
μ
8.
I
n
th
e
s
ec
o
n
d
s
tep
,
b
y
ap
p
l
y
in
g
t
h
e
Z
i
m
m
er
m
a
n
n
al
g
o
r
ith
m
o
n
t
h
e
s
u
b
co
d
e
f
i
x
ed
b
y
μ
2,
th
e
m
i
n
i
m
u
m
d
is
ta
n
ce
o
b
tain
ed
is
eq
u
al
to
3
9
,
w
h
ich
i
s
g
r
ea
t
er
th
an
t
h
e
d
esig
n
ed
d
is
tan
ce
f
o
r
th
e
co
n
s
id
er
ed
B
C
H
co
d
e.
T
h
en
w
e
p
ass
to
th
e
s
u
b
co
d
e
f
i
x
ed
b
y
th
e
s
e
co
n
d
p
er
m
u
tat
io
n
w
i
th
d
i
f
f
er
en
t
c
y
cle
s
tr
u
ct
u
r
e,
w
h
ic
h
is
h
er
e
μ
8,
b
y
ap
p
ly
in
g
t
h
e
Z
i
m
m
er
m
an
n
alg
o
r
it
h
m
o
n
th
is
s
u
b
co
d
e
,
th
e
m
i
n
i
m
u
m
d
is
tan
ce
o
b
tain
ed
is
eq
u
al
to
3
7
,
w
h
ic
h
is
eq
u
al
to
th
e
d
esi
g
n
ed
d
is
tan
ce
f
o
r
t
h
e
c
o
n
s
id
er
ed
B
C
H
co
d
e,
an
d
th
er
ef
o
r
e
th
e
m
i
n
i
m
u
m
d
is
tan
ce
is
3
7
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS
T
h
is
Sectio
n
p
r
esen
t
s
a
v
ali
d
atio
n
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
n
B
C
H
co
d
es
o
f
k
n
o
w
n
m
in
i
m
u
m
d
is
tan
ce
an
d
its
ap
p
licatio
n
f
o
r
f
in
d
in
g
t
h
e
m
i
n
i
m
u
m
d
is
ta
n
ce
o
f
B
C
H
co
d
es
o
f
u
n
k
n
o
w
n
m
in
i
m
u
m
d
i
s
tan
ce
.
T
h
is
Sectio
n
p
r
esen
ts
a
ls
o
a
co
m
p
ar
is
o
n
b
et
w
ee
n
t
h
e
p
r
o
p
o
s
ed
s
ch
e
m
e
an
d
p
r
ev
io
u
s
w
o
r
k
o
n
m
in
i
m
u
m
d
is
tan
ce
f
o
r
B
C
H
co
d
es.
A
ll
r
es
u
lt
s
h
av
e
b
ee
n
d
o
n
e
u
s
i
n
g
a
s
i
m
p
le
co
n
f
i
g
u
r
atio
n
m
ac
h
in
e
: I
n
tel(
R
)
C
o
r
e(
T
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U
C
P
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GHz
R
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GO.
T
h
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r
esu
lts
ar
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m
ad
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b
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r
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n
i
n
g
t
h
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cite
d
alg
o
r
it
h
m
i
n
1
d
a
y
f
o
r
ea
ch
co
d
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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&
C
o
m
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g
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SS
N:
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p
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1235
4
.
1
.
Va
lid
a
t
io
n
o
f
t
he
pro
po
s
ed
s
che
m
e
I
n
o
r
d
er
to
v
alid
ate
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
,
it
i
s
ap
p
lied
o
n
all
B
C
H
co
d
es
o
f
k
n
o
w
n
m
i
n
i
m
u
m
d
is
tan
ce
p
r
ese
n
ted
in
T
ab
le
1
A
l
l
th
e
n
ar
r
o
w
-
s
en
s
e
p
r
i
m
it
i
v
e
b
in
ar
y
B
C
H
co
d
es
o
f
le
n
g
th
2
5
5
h
av
e
t
h
eir
m
i
n
i
m
u
m
d
is
ta
n
ce
eq
u
al
to
th
eir
d
esig
n
ed
d
is
ta
n
ce
ex
ce
p
t
B
C
H(
2
5
5
,
6
3
,
6
1
)
,
w
h
ic
h
h
a
s
m
i
n
i
m
u
m
d
is
ta
n
ce
6
3
,
an
d
B
C
H(
2
5
5
,
7
1
,
5
9
)
,
w
h
ich
h
as
m
i
n
i
m
u
m
d
i
s
tan
ce
6
1
.
T
h
e
b
o
th
last
r
esu
lt
h
a
v
e
b
ee
n
p
r
o
v
ed
in
[
1
2
]
,
b
y
u
s
i
n
g
th
e
Ne
w
to
n
’
s
id
e
n
titi
es.
T
ab
le
1
s
u
m
m
ar
ize
s
th
e
o
b
tain
ed
r
esu
lts
.
I
t
s
h
o
w
s
t
h
at
t
h
e
m
i
n
i
m
u
m
w
ei
g
h
t
f
o
u
n
d
b
y
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
is
eq
u
al
to
th
e
tr
u
e
v
alu
e
o
f
th
e
m
in
i
m
u
m
d
i
s
tan
ce
o
f
all
B
C
H
co
d
es
o
f
len
g
t
h
2
5
5
.
T
h
er
ef
o
r
e,
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
is
v
al
id
ated
f
o
r
len
g
th
2
5
5
.
T
ab
le
1
.
V
alid
atio
n
o
f
th
e
p
r
o
p
o
s
ed
s
ch
e
m
e
B
C
H
(
n
,
k
,
δ
)
T
r
u
e
v
a
l
u
e
o
f
mi
n
i
m
u
m
d
i
s
t
a
n
c
e
d
(
Z
S
S
M
P
)
B
C
H
(
n
,
k
,
δ
)
T
r
u
e
v
a
l
u
e
o
f
mi
n
i
m
u
m
d
i
s
t
a
n
c
e
d
(
Z
S
S
M
P
)
B
C
H
(
2
5
5
,
2
4
7
,
3
)
3
3
B
C
H
(
2
5
5
,
1
1
5
,
4
3
)
43
43
B
C
H
(
2
5
5
,
2
3
9
,
5
)
5
5
B
C
H
(
2
5
5
,
1
0
7
,
4
5
)
45
45
B
C
H
(
2
5
5
,
2
3
1
,
7
)
7
7
B
C
H
(
2
5
5
,
9
9
,
4
7
)
47
47
B
C
H
(
2
5
5
,
2
2
3
,
9
)
9
9
B
C
H
(
2
5
5
,
9
1
,
5
1
)
51
51
B
C
H
(
2
5
5
,
2
1
5
,
1
1
)
11
11
B
C
H
(
2
5
5
,
8
7
,
5
3
)
53
53
B
C
H
(
2
5
5
,
2
0
7
,
1
3
)
13
14
B
C
H
(
2
5
5
,
7
9
,
5
5
)
55
55
B
C
H
(
2
5
5
,
1
9
9
,
1
5
)
15
15
B
C
H
(
2
5
5
,
7
1
,
5
9
)
*
61
61
B
C
H
(
2
5
5
,
1
9
1
,
1
7
)
17
17
B
C
H
(
2
5
5
,
6
3
,
6
1
)
*
63
63
B
C
H
(
2
5
5
,
1
8
7
,
1
9
)
19
19
B
C
H
(
2
5
5
,
5
5
,
6
3
)
63
63
B
C
H
(
2
5
5
,
1
7
9
,
2
1
)
21
21
B
C
H
(
2
5
5
,
4
7
,
8
5
)
85
85
B
C
H
(
2
5
5
,
1
7
1
,
2
3
)
23
23
B
C
H
(
2
5
5
,
4
5
,
8
7
)
87
87
B
C
H
(
2
5
5
,
1
6
3
,
2
5
)
25
25
B
C
H
(
2
5
5
,
3
7
,
9
1
)
91
91
B
C
H
(
2
5
5
,
1
5
5
,
2
7
)
27
27
B
C
H
(
2
5
5
,
2
9
,
9
5
)
95
95
B
C
H
(
2
5
5
,
1
4
7
,
2
9
)
29
29
B
C
H
(
2
5
5
,
2
1
,
1
1
1
)
1
1
1
1
1
1
B
C
H
(
2
5
5
,
1
3
9
,
3
1
)
31
31
B
C
H
(
2
5
5
,
1
3
,
1
1
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27
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51
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Co
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5
8
0
.
2
0
2
2
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8
.
2
0
2
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C
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(
1
0
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,
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2
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4
1
)
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7
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3
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7
B
C
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(
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)
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8
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(
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0
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3
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59
2
6
5
0
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1
8
6
2
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6
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)
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61
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8
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2
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C
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)
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5
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7
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8
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(
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63
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(
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69
2
7
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2
1
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4
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1
B
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(
1
0
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7
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)
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3
5
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0
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5
.
0
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(
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)
71
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B
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(
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3
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0
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3
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B
C
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(
1
0
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7
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73
2
8
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1
8
6
2
8
2
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1
8
6
B
C
H
(
1
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3
,
3
6
,
4
4
7
)
4
4
7
3
7
8
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.
0
4
6
3
7
8
.
0
4
6
B
C
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(
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75
2
7
9
0
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2
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9
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2
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9
B
C
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3
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7
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6
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6
B
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(
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7
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2
8
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4
9
2
8
2
.
2
4
9
B
C
H
(
1
0
2
3
,
1
6
,
4
9
5
)
4
9
5
3
7
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0
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1
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2
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3
1
B
C
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(
1
0
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,
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8
,
7
9
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79
2
7
9
0
.
2
6
4
2
7
9
.
2
6
4
B
C
H
(
1
0
2
3
,
1
1
,
5
1
1
)
5
1
1
3
4
8
0
.
0
3
0
3
4
8
.
0
3
0
B
C
H
(
1
0
2
3
,
6
4
8
,
8
3
)
83
3
5
2
0
.
3
4
2
3
5
2
.
3
4
2
5.
CO
NCLU
SI
O
N
AN
D
P
E
RS
P
E
CT
I
VE
S
I
n
th
i
s
p
ap
er
,
w
e
h
av
e
p
r
o
p
o
s
ed
a
n
e
w
ef
f
ic
ien
t
s
ch
e
m
e
to
f
i
n
d
th
e
m
in
i
m
u
m
d
is
ta
n
ce
f
o
r
lar
g
e
B
C
H
co
d
es.
T
h
e
ex
p
er
i
m
e
n
tal
r
es
u
lts
s
h
o
w
th
at
t
h
e
p
r
o
p
o
s
ed
s
ch
e
m
e
o
u
tp
er
f
o
r
m
s
s
ev
er
a
l
k
n
o
w
n
p
o
w
er
f
u
l
tech
n
iq
u
es.
T
h
e
tr
u
e
v
al
u
e
o
f
th
e
m
in
i
m
u
m
d
i
s
ta
n
ce
s
an
d
c
o
n
s
eq
u
e
n
tl
y
th
e
er
r
o
r
co
r
r
e
cti
n
g
ca
p
ab
ilit
y
o
f
all
th
e
1
6
5
B
C
H
co
d
es
o
f
le
n
g
t
h
u
p
to
1
0
2
3
ar
e
d
eter
m
i
n
ed
ex
ce
p
t
th
e
t
w
o
ca
s
es
o
f
t
h
e
B
C
H(
5
1
1
,
1
4
8
)
an
d
B
C
H(
5
1
1
,
2
5
9
)
c
o
d
es.
I
n
th
e
p
er
s
p
ec
tiv
es
o
f
t
h
is
w
o
r
k
,
w
e
w
il
l
ap
p
l
y
t
h
is
p
o
w
er
f
u
l
s
ch
e
m
e
to
co
n
s
tr
u
ct
g
o
o
d
lar
g
e
c
y
clic
co
d
es,
an
d
ad
ap
t th
is
s
ch
e
m
e
to
co
m
p
u
te
t
h
e
m
i
n
i
m
u
m
d
is
ta
n
ce
f
o
r
o
th
er
lin
ea
r
co
d
es.
RE
F
E
R
E
NC
E
S
[1
]
C.
S
h
a
n
n
o
n
.
"
A
M
a
th
e
m
a
ti
c
a
l
T
h
e
o
ry
o
f
Co
m
m
u
n
ica
ti
o
n
,
"
Bell
S
y
st.
T
e
c
h
.
J
.
,
2
7
:
6
2
3
–
6
5
9
,
j
u
il
let
e
t
o
c
to
b
re
1
9
4
8
.
[2
]
W
a
q
a
s
A
.
I
m
ti
a
z
a
n
d
N.
A
h
m
a
d
"
Ca
rd
in
a
li
ty
En
h
a
n
c
e
m
e
n
t
o
f
S
A
C
-
OCD
M
A
S
y
ste
m
s
Us
in
g
n
e
w
Di
a
g
o
n
a
l
Do
u
b
le
W
e
ig
h
t
Co
d
e
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
C
o
mm
u
n
ica
ti
o
n
Ne
tw
o
rk
s a
n
d
I
n
fo
rm
a
t
io
n
S
e
c
u
rity
,
V
o
l
6
,
No
.
3
,
2
0
1
4
.
[3
]
A
.
V
a
rd
y
,
“
T
h
e
in
trac
tab
il
it
y
o
f
Co
m
p
u
ti
n
g
th
e
M
in
im
u
m
d
istan
c
e
o
f
a
Co
d
e
,
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
In
f
o
rm
a
ti
o
n
T
h
e
o
r
y
,
”
v
o
l.
4
3
,
No
.
6
,
p
p
.
1
7
5
7
–
1
7
6
6
,
1
9
9
7
.
[4
]
S
a
ïd
No
u
h
,
I
d
riss
Ch
a
n
a
a
n
d
M
o
sta
f
a
Be
l
k
a
s
m
i
,
"
De
c
o
d
in
g
o
f
Blo
c
k
Co
d
e
s
b
y
u
sin
g
G
e
n
e
ti
c
A
l
g
o
rit
h
m
s
a
n
d
P
e
rm
u
tatio
n
s
S
e
t
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Co
mm
u
n
ica
t
io
n
Ne
t
wo
rk
s
a
n
d
I
n
fo
rm
a
ti
o
n
S
e
c
u
rity
,
Vo
l
5
,
No
.
3
,
2
0
1
3
.
[5
]
R
o
o
p
a
li
A
g
a
r
w
a
l,
M
a
n
o
j
K.
S
h
u
k
la,
"
SC
-
F
DM
-
IDMA
S
c
h
e
m
e
E
m
p
lo
y
in
g
BCH
Co
d
in
g
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
),
V
o
l
.
7
,
No
.
2
,
p
p
.
9
9
2
-
9
9
8
,
A
p
ril
2
0
1
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il 2
0
1
9
:
1
2
3
2
-
1239
1238
[6
]
S
o
f
i
Na
i
m
a
,
De
b
b
a
t
F
a
ti
m
a
,
Be
n
d
im
e
ra
d
F
e
th
i.
Tarik
"
P
e
rf
o
r
m
a
n
c
e
I
m
p
ro
v
e
m
e
n
t
o
f
M
IM
O
-
OS
TBC
S
y
ste
m
w
it
h
BCH
-
T
URBO
Co
d
e
In
Ra
y
leig
h
F
a
d
in
g
Ch
a
n
n
e
l
"
,
In
d
o
n
e
si
a
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
a
n
d
Co
mp
u
ter
S
c
ien
c
e
,
Vo
l.
1
1
,
No
.
3
,
p
p
.
8
9
8
-
9
0
7
,
S
e
p
tem
b
e
r
2
0
1
8
.
[7
]
C.
Din
g
,
X
.
D
u
,
Z.
Zh
o
u
,
"
T
h
e
Bo
se
a
n
d
M
in
im
u
m
Dista
n
c
e
o
f
a
Clas
s
Of
BCH
Co
d
e
s
,"
IEE
E
T
ra
n
s.
In
f
.
T
h
e
o
ry
,
V
o
l
.
6
1
,
Iss
u
e
5
,
p
p
.
2
3
5
1
–
2
3
5
6
,
M
a
y
2
0
1
5
.
[8
]
C.
Din
g
,
"
P
a
ra
m
e
ters
o
f
S
e
v
e
ra
l
Clas
se
s o
f
BCH
Co
d
e
s
,
"
IEE
E
T
r
a
n
s.
In
f
.
T
h
e
o
ry
,
V
o
l.
6
1
,
No
.
1
0
,
p
p
.
5
3
2
2
–
5
3
3
0
,
Oc
to
b
e
r
2
0
1
5
.
[9
]
Cu
n
sh
e
n
g
Din
g
,
Cu
il
i
n
g
F
a
n
,
Z
h
e
n
g
c
h
u
n
Zh
o
u
"
T
h
e
Di
m
e
n
sio
n
a
n
d
M
i
n
im
u
m
Dista
n
c
e
o
f
Tw
o
Clas
se
s
o
f
P
rim
it
iv
e
BCH C
o
d
e
s
,"
Fi
n
i
te F
i
e
ld
s a
n
d
T
h
e
ir
A
p
p
li
c
a
ti
o
n
s
,
Vo
l.
4
5
,
p
p
.
2
3
7
-
2
6
3
,
M
a
y
2
0
1
7
.
[1
0
]
Ha
o
L
iu
,
Cu
n
sh
e
n
g
Din
g
,
C
h
e
n
g
ju
L
i
"
Dim
e
n
sio
n
s
o
f
T
h
re
e
Ty
p
e
s
o
f
BCH
Co
d
e
s
Ov
e
r
G
F
(q
)
,"
Disc
re
t
e
M
a
th
e
ma
ti
c
s
,
V
o
l.
3
4
0
,
Iss
u
e
8
,
p
p
.
1
9
1
0
-
1
9
2
7
,
A
u
g
u
st
2
0
1
7
.
[1
1
]
P
.
Ch
a
rp
i
n
"
Op
e
n
p
ro
b
lem
s
o
n
c
y
c
li
c
c
o
d
e
s
"
,
in
:
V
.
S
.
P
les
s,
W
.
C.
Hu
ffm
a
n
(Ed
s.),
Ha
n
d
b
o
o
k
o
f
Co
d
i
n
g
T
h
e
o
r
y
,
V
o
l
.
I,
No
rt
h
-
Ho
ll
a
n
d
,
p
p
.
9
6
3
–
1
0
6
3
(C
h
a
p
ter1
1
),
1
9
9
8
.
[1
2
]
Da
n
iel
A
u
g
o
t,
P
a
sc
a
le
Ch
a
rp
in
,
a
n
d
Nic
o
las
S
e
n
d
r
ier
"
S
tu
d
y
in
g
th
e
L
o
c
a
to
r
P
o
ly
n
o
m
ials
o
f
M
in
im
u
m
W
e
i
g
h
t
Co
d
e
w
o
rd
s o
f
BCH Co
d
e
s
,"
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
I
n
fo
rm
a
ti
o
n
T
h
e
o
ry
,
V
o
l.
3
8
,
N
o
.
3
,
M
a
y
1
9
9
2
.
[1
3
]
Ch
a
b
a
u
d
F
.
"
A
s
y
m
p
to
ti
c
A
n
a
l
y
sis
o
f
P
ro
b
a
b
il
isti
c
A
lg
o
rit
h
m
s
f
o
r
F
in
d
i
n
g
S
h
o
rt
C
o
d
e
w
o
rd
s.
"
In
:
Ca
m
io
n
P
.
,
Ch
a
rp
in
P
.
,
Ha
ra
ri
S
.
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