Tải bản đầy đủ (.pdf) (12 trang)

Mã vòng - Cyclic codes ppsx

Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (126.85 KB, 12 trang )

M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
!

M· vßng – Cyclic codes
I/ M« t¶
"# $%&' ()*+,-+ )./012 ,3 456 78 4# +9 :&' /;&' <=+ >-?6 @5&' @#- 6@.&' 67A&' 6-&B
"# +9 6C& '8- ,3 +*+,-+ $D /. +9 <=+ 6E&7 /F+7 $%&' +GH 456 6I 4# +J&' ,3 456 6I 4#B
"# $%&' (7H* 4# +7K LM2 +%& <NO+ '8- 456 ,PQ +.& RKH& 6@8&' +GH 4# 6K*S& 6E&7B "#
&3* <T&' +7U V $D 7H- ,V /. 1HK <W*X
Y "Z+7 4# 7.T $3 6E&7 1*&/@.40 (75- +7:&'2 +9 67[ <NO+ 67\+ 7-?& /] /3&' &7^ >5
'7- /F+7 +9 7_- 6-SQ (`00/>H+L +.&&0+6 &2B
Y a7^ +bK 6@U+ +GH 4# +9 67[ 6D4 <NO+ &7-cK Q7Nd&' Q7TQ <[ '-e- 4#B
"5/(!/+(624 "56 4# 6K*S& 6E&7 )(&f L2 <NO+ + ,3 4# $%&' &SK 4g- ,h& /F+7 $%&'
456 6I 4# +GH ) 67D LS6 RKe +J&' ,3 456 4# $i+ 6d +GH )B
)7. $i+ 6d 4# $ j ($
k
f$
!f
BBB$
&Y!
2f +T+ 673&7 Q7h& +GH $i+ 6d 4# &3* +9 67[ l04 &7N ,3 7?
1m +GH <H 67:+ $(l2X $(l2 j $
k
n $
!
l n BBB n $
&Y!
l
&Y!


B
op* 4g- $i+ 6d 4# $ +9 +7-cK /3- & 6Nd&' :&' $P- <H 67:+ 4# $(l2 +9 >p+ &7q 7d&
7.=+ >r&' &Y!B aSK $
&Y!
≠ k 67D >p+ +GH $(l2 ,3 &Y!f &SK $
&Y!
j k 67D >p+ +GH $(l2 &7q 7d& $
&Y
!
B s\ 6Nd&' <Nd&' '-tH $i+ 6d 4# $ $3 <H 67:+ 4# $(l2 ,3 !Y!f $(l2 <NO+ '8- ,3 <H 67:+ 4#
(+./0 Q.,*&.4-H,2 +GH $i+ 6d 4# $B u7- <9 6I $i+ 6d 4# $3 6I <H 67:+ 4# <NO+ 1v /;&' &7N
&7HKB
78!9:4 "# 6K*S& 6E&7 w >e&' ! <NO+ ' ,3 4# $%&'
u7m- 6-& oi+ 6d 4#X $ xH 67:+ 4# $(l2
(kkkk2 (kkkkkkk2 k j kB'(l2
(!kkk2 (!!k!kkk2 ! n l nl
y
j '(l2
(k!kk2 (k!!k!kk2 l n l
z
n l
{
j lB'(l2
(!!kk2 (!k!!!kk2 ! n l
z
n l
y
n l
{
j (! n l2B'(l2

(kk!k2 (kk!!k!k2 l
z
n l
y
n l
|
j l
z
B'(l2
(!k!k2 (!!!kk!k2 ! n l n l
z
n l
|
j (! n l n l
z
2B'(l2
(k!!k2 (k!k!!!k2 l n l
y
n l
{
nl
|
j (! nl n l
z
2B'(l2
(!!!k2 (!kkk!!k2 l
y
n l
{
n l

}
j l
y
B'(l2
(kkk!2 (kkk!!k!2 ! n l n l
{
n l
}
j (! n l
y
2B'(l2
(!kk!2 (!!kk!k!2 l n l
z
n l
y
n l
}
j (l n l
y
2B'(l2
(k!k!2 (k!!!kk!2 l n l
z
n l
}
j (! n l n l
y
2B'(l2
(!!k!2 (!k!kkk!2 ! n l
z
n l

}
j (!n l n l
y
2B'(l2
M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
z

(kk!!2 (kk!k!!!2 l
z
n l
{
n l
|
n l
}
j (l
z
n l
y
2B'(l2
(!k!!2 (!!!!!!!2 ! n l n l
z
n l
y
n l
{
n l
|

n l
}
j (! n l
z
n l
y
2B'(l2
(k!!!2 (k!kkk!!2 l n l
|
n l
}
j (l n l
z
n l
y
2B'(l2
(!!!!2 (!kk!k!!2 ! n l
y
n l
|
n l
}
j (! n l n l
z
n l
y
2B'(l2
;</+!=4!>?!@A/+!@B*!C2!D(EF!G*/(!+HIJ!K!=!L!I!L!I
M


Mét sè tÝnh chÊt ®¹i sè quan träng cña m· vßng:
"5/(!3N!=4!xH 67:+ 4# L7T+ k +9 >p+ &7q &7b6 +GH 4# $%&' ,3 /K* &7b6B
"5/(!3N!O4 aSK '(l2 j '
k
n '
!
l n BBB n '
@Y!
l
@Y!
n l
@
,3 <H 67:+ 4# &7q &7b6 +GH 4# $%&'
)(&f L2 67D 7? 1m '
k
>~6 >K5+ Q7e- >r&' !B
"5/(!3N!M4!)7. '(l2 j ! n '
!
l n '
z
l
z
n BBB n l
@
,3 <H 67:+ 4# L7T+ k +9 >p+ &7q &7b6
+GH 4# $%&' )(&f L2f 456 <H 67:+ &7F Q7W& +9 >p+ &7q 7d& 7.=+ >r&' &Y! ,3 <H 67:+ 4#
&SK $3 +7• &SK &9 ,3 >5- +GH '(l2B
"5/(!3N!P4!)7. 4# $%&' )(&fL2f 6_& 6Z- 456 $3 +7• 456 <H 67:+ 4# +9 >p+ & Y LX
'(l2 j ! n '
!

l n '
z
l
z
n BBB n '
&YLY!
l
&YLY!
n l
&YL
B
"5/(!3N!Q4!xH 67:+ 1-&7 '(l2 +GH 456 4# $%&' )(&fL2 ,3 456 67IH 1m +GH l
&
n!B
"5/(!3N!R4 aSK '(l2 ,3 <H 67:+ >p+ (&YL2 $3 ,3 456 67IH 1m +GH l
&
n! 67D '(l2 1-&7 @H 4#
$%&' )(&f L2B
M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
y

II/ Ma trËn sinh vµ ma trËn kiÓm tra cña m· vßng.
G8- '(l2 ,3 <H 67:+ 1-&7 >p+ &YL +GH 4# $%&' )(&fL2B "56 L7m- /t ,-?K L Q7h& 6v (4
k
f
4
!
fBBB 4

LY!
2 +9 67[ <NO+ l04 ,3 456 <H 67:+ 67A&' 6-&X 4(l2 j 4
k
n 4
!
l n BBB n 4
LY!
l
LY!
B o-?+
4# 7.T 67A&' RKH $-?+ &7W& <H 67:+ 67A&' 6-& $P- <H 67:+ 1-&7B uS6 RKe 6H +9X
)
4
j (+
k
f +
!
f BBB +
&Y!
2
)
4
(l2 j 4(l2B'(l2 j +
k
n +
!
Bl n BBB n +
&Y!
Bl
&Y!


TE+7 <H 67:+ 6@C& <NO+ >-[K /-]& /NP- /Z&' 6E+7 4H 6@p& &7NX
)
4
(l2 j 4(l2B'(l2 j (4
k
n 4
!
Bl n BBB n 4
LY!
Bl
LY!
2B'(l2
j 4
k
B'(l2 n 4
!
BlB'(l2 n BBB n 4
LY!
Bl
LY!
B'(l2
'(l2
lB'(l2
j [4
k
n 4
!
Bl n BBB n 4
LY!

Bl
LY!
]B B
B
l
LY!
B'(l2
DZ&' 6æ&' RKT6 +GH 4H 6@p& 1-&7 G +GH 4# $%&' )(&fL2 ,3X
'
k
'
!
'
z
BBB BBB BBB BBB '
&YL
k k BBB k
k '
k
'
!
BBB BBB BBB BBB BBB '
&YL
k BBB k
G j k k '
k
'
&YL
BBB k
BB BB BB BB BB BB BB BB BB BB BB BB

k k k BB k '
k
'
&YL

( $P- '
k
j '
&YL
j !2
T@N^&' 7OQ 6æ&' RKT6 G L7A&' +9 /Z&' 7? 67m&'B TK* &7-C& +9 67[ +7K*[& G $c /Z&'
7? 67m&' >r&' Q7iQ >-S& <æ- 73&' +GH 4H 6@p&B
78!9:4 Xi6 4# $%&' )(7f {2 +7. w >e&' ! $P- <H 67:+ 1-&7 '(l2 j ! n l n l
y
+9 4H 6@p&
&7N 1HKX
! ! k ! k k k
G j k ! ! k ! k k
k k ! ! k ! k
k k k ! ! k !
TH 67b* G L7A&' +9 /Z&' 7? 67m&'B
a7N&' &SK /ï&' Q7iQ >-S& <æ- 73&'X 7
y
j 7
y
n 7
!
$3 7
{
j 7

{
n 7
!
n 7
z
6H 67K <NO+
"H 6@p& G

+9 /Z&' 7? 67m&' &7N 1HKX
M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
{

! ! k ! k k k
G

j k ! ! k ! k k
! ! ! k k ! k
! k ! k k k !
oP- '(l2 ,3 67IH 1m +GH l
&
n !f +9X l
&
n ! j '(l2B7(l2
oP- <H 67:+ 7(l2 +9 >p+ ,3 L <NO+ >-[K /-]& &7N 1HKX
7(l2 j 7
k
n 7
!

Bl n BBB n 7
L
Bl
L
f ($P- 7
k
j 7
L
j !2
)7. $ j ($
k
f $
!
fBBB $
&Y!
2 ,3 $i+ 6d 4# +GH )B u7- <9 $(l2 j 4(l2B'(l2B a7W& $(l2 $P- 7(l2
6H <NO+X
$(l2B7(l2 j H(l2B'(l2B7(l2
j H(l2B(l
&
n !2
j H(l2 n l
&
BH(l2
D. >p+ +GH $(l2 &7q 7d& 7.=+ >r&' LY! &C& +T+ '-T 6@F +GH l
L
f l
Ln!
f BBBl
&Y!

L7A&' +9
6@.&' >-[K 67:+ 4(l2 n l
L
B4(l2B aSK L7H- 6@-[& LS6 RKe $(l2B7(l2 67D 7? 1m l
L
f l
Ln!
fBBB l
&
Q7e-
>r&' kB D. <9 &7p& <NO+ &YL Q7Nd&' 6@D&7 1HKX
∑7
-
$
&Y-Yj
j kf $P- - ≤ j ≤ &YLB
H34 1m &'NO+ +GH 7(l2 ,3X
l
L
B7(l
Y!
2 j 7
L
n 7
LY!
l n 7
LYz
l
z
n BBB n 7

k
l
L

D] /3&' &7p& 67b* @r&' l
L
7(l
Y!
2 +J&' ,3 67IH 1m +GH (l
&
n !2B op* <H 67:+ 1-&7 l
L
7(l
Y!
2
1-&7 @H 4# $%&' (&f&YL2 $P- 4H 6@p& H(&YL2 l & ,3 4H 6@p& 1-&7X
7
L
7
LY!
7
LYz
BBBBB 7
k
k BBBB k
k 7
L
7
LY!
7

LYz
BBB 7
k
BBBB k
H j k k 7
L
7
LY!
7
LYz
BBBB 7
k
BBB k
BBB
k k BBBk 7
L
7
LY!
7
LYz
BBB 7
k

Bb6 LM $i+ 6d 4# &3. +GH ) <cK 6@\+ '-H. $P- 4g- 73&' +GH HB D. <9 H ,3 4H 6@p&
L-[4 6@H +7½& ,Î +GH 4# $%&' )B D. H &7p& <NO+ 6ï <H 67:+ 7(l2 &C& 7(l2 <NO+ '8- ,3 <H
67:+ L-[4 6@H +GH )B
"5/(!3N!S4!G8- ) ,3 4# $%&' (&fL2 $P- <H 67:+ 1-&7 '(l2B "# <m- &'ÉK +GH ) +J&' ,3
4# $%&' $3 <NO+ 1-&7 @H >w- <H 67:+X l
L
B7(l

Y!
2 $P- 7(l2 j (l
&
n !2/'(l2B
M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
|

III/ M· ho¸ m· vßng
"# 7.T 4# $%&' (&fL2 /Z&' 7? 67m&' '_4 >H >NP+X
;TBF!=4!a7W& <H 67:+ 67A&' 6-& K(l2 $P- l
&YL
B
;TBF!O4 )7-H l
&YL
BK(l2 +7. '(l2 &7p& <NO+ Q7h& /N >(l2B
;TBF!M4 HD&7 673&7 6I 4# >(l2 n l
&YL
BK(l2B
Tb6 +e >H >NP+ &3* +9 67[ 67\+ 7-?& >r&' 4Z+7 +7-H $P- 67H&7 '7- /F+7 &YL 6h&' +9
734 7_- 6-SQ 6Nd&' :&' $P- <H 67:+ 1-&7 '(l2X
'(l2 j ! n '
!
l n '
z
l
z
nBBB n '
&YLY!

l
&YLY!
n l
&YL
B
sd <_ 4# 7.T <NO+ +7• 6@.&' 7D&7 !
U,-!TBF4
L3 456 L7WK +GH 67H&7 '7- /F+7 (`,-QY`,.Q2

)æ&' +5&' 4./K,Yz
(XOR2

"m- ,-C& LS6 (' j kX
L7A&' +9 1\ ,-C& LS6f ' j ! +9 1\ ,-C& LS62







H×nh 1: "Z+7 4# 7.T $%&' (&fL2 $P- <H 67:+ 1-&7X
'(l2 j ! n '
!
Bl n '
z
Bl
z
n BBB n '
&YLY!

Bl
&YLY!
n l
&YL

&)F!VTBF!DWX!1?!9Y/+!C2!D(EF!G*/(!/(T!G2,4!
;TBF!=4!)æ&' <9&' (+7. 67A&' 6-& RKH2f L +7t 1m 67A&' 6-&X K
k
f K
!
fBBB K
LY!
(7H* w /Z&'
<H 67:+ ,3X K(l2 j K
k
n K
!
l n K
z
l
z
n BBB n K
LY!
l
LY!
2 <NO+ /F+7 $3. 4Z&' $3 <%&' 67^- &m- $3.
LC&7 6@K*c&B DF+7 67A&' 6-& K(l2 $3. 4Z+7 6I 67-S6 >F <hK +Km- <[ &7W& 6@NP+ K(l2 $P- l
&YL
B
a'H* 1HK L7- 67A&' 6-& <NO+ <NH $3. 4Z+7 67D & Y L +7t 1m +%& ,Z- 6@.&' 67H&7 '7- ,3 &7t&'

1m L-[4 6@H +7½& ,ÎB
>
k
>
&YLY!
>
z
>
!
)æ&'

'
k
j!

'
!

'
z

'
&YLY!

T7A&' 6-& l
&
Y
L
BK(l2


)T+ 1m L-[4 6@H
+7½& ,Î
TI 4#

M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
}

;TBF!O4 )~6 <:6 <N^&' 7_- 6-SQ >r&' +T+7 <-cK L7-[& +7. +T+ +æ&' '
-
(7w L7A&' +7.
67A&' 6-& RKH2B
;TBF!M4!DF+7 &7t&' +.& 1m L-[4 6@H +7½& ,Î $3 <NH @H <N^&' 6@K*c&B )T+ +7t 1m L-[4
6@H &3* LS6 7OQ $P- L +7N+ 1m 67A&' 6-& 6Z. 673&7 $i+ 6d 4#B
78!9:4 Xi6 456 4Z+7 4# 7.T 4# $%&' (7f{2 $P- <H 67:+ 1-&7 '(l2 j ! n l n l
y
&7N
7D&7 z







H×nh 2: "Z+7 4# 7.T 4# $%&' (& j 7f L j {2 $P- <H 67:+ 1-&7 '(l2 j ! n l n l
y
o-?+ 4# 7.T 4# $%&' +J&' +9 67[ 67\+ 7-?& >r&' +T+7 1v /;&' <H 67:+ L-[4 6@H +7½&
,Î 7(l2 j 7

k
n 7
!
Bl n BBB n 7
L
Bl
L
B )9 67[ + +A&' 67:+X
o
&YLYj
j ∑7
-
$
&Y-Yj
j k f $P- - ≤ j ≤ &YL ,3 ,Kp6 <[ lT+ <F&7 &YL +7t 1m L-[4 6@H +7½& ,Î $
k
f
$
!
fBBB $
&YLY!
B HD&7 y ,3 4Z+7 4# 7.T +9 7? 1m 7(l2 ,3 +T+ LS6 &m- 7_- 6-SQB
'+, /!3N!(XWD!CZ/+!F[2!1WF(!@\!F)F!VTBF!1?!(]2!9Y/+!C2!D(EF!^*_1!D`2!/(T!
G2,4!
;TBF!=4 )æ&' ! <9&'f +æ&' z 7wf L +7t 1m 67A&' 6-& K(l2 j K
k
n K
!
l n BBB nK
LY!

l
LY!
<NO+
/F+7 $3. 67H&7 '7- <_&' 67^- 6@K*c& @H LC&7 67A&' 6-&B
;TBF!O4 a'H* 1HK L7- 6.3& >5 +T+ +7t 1m 67A&' 6-& <NO+ /F+7 $3. 67H&7 '7-B )æ&' !
7wf +æ&' z <9&'f +7t 1m L-[4 6@H <hK 6-C& ,3X
o
&YLY!
j 7
k
B$
&Y!
n 7
!
B$
&Yz
n BBB n 7
LY!
B$
&YL

K
LY!
n 7
!
BK
LYz
n BBBn 7
LY!
BK

k

o
&YLY!
<NO+ 6Z. 673&7 $3 lKb6 7-?& 6Z- <-[4 PB
;TBF!M4!T7H&7 '7- /F+7 $%&' 456 >-6f +7t 1m L-[4 6@H <NO+ /F+7 $3. LC&7 67A&' 6-& $3
<_&' 67^- +J&' /F+7 $3. 67H&&7 '7-f +7t 1m L-[4 6@H 67: 7H- ,3X
o
&YLYz
j 7
k
B$
&Yz
n 7
!
B$
&Yy
n BBBB n 7
LY!
B$
&YL

j K
LYz
n 7
!
BK
LYy
n BBB n 7
LYz

BK
k
n 7
LY!
BK
&YLY!
B
o
&YLYz
<NO+ 6Z. 673&7 $3 lKb6 7-?& 6Z- /-[4 PB
)T+ 1m L-[4 6@H
+7½& ,Î
>
k
>
z
>
!
)æ&'

'
k
j!

'
!

T7A&' 6-& l
&
Y

L
BK(l2

TI 4#

M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
7

;TBF!P4 L=Q ,Z- >NP+ y +7. <S& L7- &YL +7t 1m L-[4 6@H <NO+ 6Z. @H $3 /F+7 $3. LC&7
67A&' 6-&B







H×nh 3: "Z+7 4# 7.T 4# $%&' (&f L2 /\H $3. <H 67:+ L-[4 6@H 7(l2 j ! n 7
!
Bl n BBB n l
L

"_!1*/(!(XWa!IbD!@8!9:!G2,4!
HD&7 { ,3 1d <_ 4# 7.T +7. 4# $%&' (7f{2 +9 <H 67:+ 1-&7 '(l2 j ! n l n l
y
/\H $3. <H
67:+ L-[4 6@HX 7(l2 j l
7

/! n l n l
y
j ! n l n l
z
n l
{

"g- 6I 4# +9 /Z&' $ j ($
k
f $
!
f $
z
f $
y
f $
{
f $
|
f $
}
2 $P- $
y
f $
{
f $
|
f $
}
,3 &7t&' +.& 1m +GH

67A&' 6-&f +%& $
k
f $
!
f $
z
,3 &7t&' +.& 1m L-[4 6@H +7½& ,Î (QH@-6*2f Q7Nd&' 6@D&7 lT+ <F&7
>w- &7t&' +.& 1m L-[4 6@H ,3X
o
yYj
j !B$
7Yj
n !B$
}Yj
n !B$
|Yj
n kB$
{Yj

j $
7Yj
n $
}Yj
n $
|Yj
f $P- ! ≤ j ≤ y
G-e 1v 67A&' 6-& +h& 4# 7.T ,3 (!k!!2 67DX $
y
j !f $
{

j kf $
|
j !f $
}
j !B
)7t 1m L-[4 6@H <hK 6-C& ,3X $
z
j $
}
n $
|
n $
{
j ! n ! n k j k
)7t 1m L-[4 6@H 67: 7H- ,3X $
!
j $
|
n $
{
n $
y
j ! n k n !
)7t 1m L-[4 6@H 67: >H ,3X $
k
j $
{
n $
y
n $

z
j k n ! n k j !
oD $p* 6I 4# 6Nd&' :&' $P- 67A&' 6-& (!k!!2 ,3 (!kk!k!!2








H×nh 4: "Z+7 4# 7.T $%&' (&j7f Lj{2 /\H $3. <H 67:+ L-[4 6@H (HIJ!K!=!L!I!L!I
O
!L!I
P
!
)æ&'!

)æ&'z

o
&YL
o
&Yz
o
&Y(LY!2
o
&Y!
7
LY!

7
LYz
7
z
7
k
7
k
j!

xhK
$3.
P

xhK @HX o
&YLY!
f o
&YLYz
fBB

)æ&'!

)æ&'z




7
k
j!


xhK
$3.
P

xhK @HX
!kk!k!!


7
z
j!

7
!
j!

M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
8

IV/ Gi¶i m· vßng
o-?+ '-e- 4# $%&' >H. '_4 >H >NP+ &7N $-?+ '-e- 4# L7m- 6K*S& 6E&7X
;TBF!=4!TE&7 s*&/@.40B
;TBF!O4!D\H $3. 1*&/@.40 <[ lT+ <F&7 $i+6d ,g-B
;TBF!M4!svH ,g-f 67\+ 7-?& Q7iQ +5&' 4./K,Yz '-tH $i+6d ,g- $3 $i+6d &7p& <NO+B uS6
RKe ,3 $i+6d 67A&' 6-& 67\+ 1\ <NO+ 6@K*c& <-B aSK 1vH 6Kh& 6\ 6I&' >-6 456 67D +7• +h& 456
+æ&' XORB a'NO+ ,Z- &SK 67\+ 7-?& 456 +T+7 1vH 1.&' 1.&' 67D Q7e- /ï&' & +æ&' XORB
)bK 6@U+ 4# $%&' +7. Q7iQ '-e- 4# $i+6d &7p& @(l2 j @

k
n @
!
l n @
z
l
z
n BBBB n @
&Y!
l
&Y!
456
+T+7 6Kh& 6\B a7t&' >-6 &7p& <NO+ 1Ï <NO+ '-e- 4# ,h& ,NO6 >w- +ï&' 456 4Z+7 '-e- 4#B
a'H* 1HK L7- 6E&7 1*&/@.4B "Z+7 '-e- 4# L-[4 6@H 1\ 6Nd&' :&' +GH 1*&/@.40 1(l2
$P- $i+6d 1vH <NO+ 0(l2 j 0
k
n 0
!
l n 0
z
l
z
nBBB n0
&Y!
l
&Y!
$P- 456 ,g- 1H- w $F 6@E +H. &7b6 l
&Y!

(0

&Y!
j !2B aSK 1(l2 L7A&' +9 1H- w $F 6@E >p+ +H. &7b6 (0
&Y!
≠k2 67D ,NK '-t 6@.&' 67H&7 '7-
<?4 (>K``0@ @0'-160@2 $3 <_&' 67^- 67H&7 '7- 1K&/@.40 /F+7 <- 456 ,h&B Br&' +T+7 &3*f
@
(!2
(l2 j @
k
l n @
!
l
z
n BBB n @
&Yz
l
&Y!
$3 <H 67:+ 1*&/@.40 4P- +GH @
(!2
(l2 ,3 1
(!2
(l2B LU+ <9 >-6 67:
7H- @
&Yz
+GH @(l2 6@w 673&7 >-6 67: &7b6 +GH @
(!2
(l2B "Z+7 '-e- 4# 6Nd&' 6\ 1Ï L-[4 6@H 1
(-2
(l2
+9 6Nd&' <Nd&' $P- $i+6d 1H- 1m $P- ,g- 6Z- $F 6@E l

&Y!
7H* L7A&'B
aSK 1*&/@.40 1(l2 +GH @(l2 6Nd&' :&' $P- 456 $i+6d 1H- $P- ,g- 1H- w $F 6@E l
&Y!
67D >-6
<hK 6-C& &7p& <NO+ @
&Y!
,3 >-6 1H- $3 &9 Q7e- <NO+ 1vH +7. <U&'B o-?+ 1vH 1HK <NO+ 67\+ 7-?&
RKH $-?+ 6E&7 6æ&' @
&Y!
⊕0
&Y!
B xH 67:+ 1vH ,g- ,3X
@
!
(l2 j @
k
n @
!
l n @
z
l
z
n BBB n @
&Yz
l
&Y!
n (@
&Y!
⊕0

&Y!
2l
&Y!
B
sHK <9 ,g- 1H- w >-6 0
&Y!
<NO+ l.T >q L7q- 1*&/@.40 1(l2B o-?+ &3* 67\+ 7-?& >r&' $-?+
+5&' 4./K, 1*&/@.40 +GH 0

(l2 j l
&Y!
$P- 1(l2B uS6 RKe +5&' &3* ,3 <H 67:+ <# 1vH 1H- @
!
(l2B
T-SQ 670. /F+7 $%&' @
!
(l2 $3 <_&' 67^- /F+7 $%&' 67H&7 '7- 1*&/@.40B uS6 RKe $-?+ /F+7
$%&' 67K <NO+ @
!
(!2
(l2 j (@
&Y!
⊕0
&Y!
2 n @
k
l n BBBn @
&Yz
l
&Y!

!
oD 67S &SK ! <NO+ 67C4 $3. 6p& +ï&'>C& 6@T- +GH 67H&7 '7- 1K&/@.40 6@.&' L7- /F+7
$%&' 67D 67K <NO+ 1
!
(!2
(l2B "Z+7 '-e- 4# >~6 <hK '-e- &7t&' >-6 &7p& <NO+ @
&Yz
B o-?+ '-e- 4#
@
&Yz
$3 +T+ ,.Z- >-6 +%& ,Z- <cK <NO+ 6E&7 '-m&' &7N '-e- 4# @
&Y!
B u7- 456 ,g- <NO+ Q7T6 7-?&
$3 1vHf &9 1Ï ,3 +7. 1*&/@.40 67H* <æ-B QKT 6@D&7 '-e- 4# 1Ï &'I&' 1HK & ,h& /F+7 $%&'B
aSK 0(l2 ,3 $i+6d ,g- <# <NO+ 1vH 67D 67H&7 '7- 1*&/@.40 1Ï >r&' kB uS6 67U+ RKT 6@-&'7`
'-e- 4# 1Ï &7p& <NO+ @(l2 <NO+ '-e- 4# +7E&7 lT+B aSK LS6 67U+ RKT 6@D&7 '-e- 4# 43
1*&/@.40 L7T+ k 67D ,g- 1H- <NO+ Q7T6 7-?& $3 L7A&' 1vH 1H- <NO+B
B5 '-e- 4# $%&' (&fL2 +9 1d <_ &7N 7D&7 | '_4 +T+ L7m-X
M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
9

Y T7H&7 '7- 1*&/@.40B
Y B5 Q7T6 7-?& $i+6d ,g-B
Y T7H&7 '7- <?4 ,NK '-t $i+6d &7p&B











H×nh 5: B5 4# $%&' $P- <H 67:+ &7p& <NO+ w <hK 67K @(l2 <NO+ /F+7 $3. 67H&7 '7-
1*&/@.40 6I >C& 6@T-B
%([!D:F!Gc2!3d*!CTeF!1f!D<!/(T!G2,4
;TBF!=4! s*&/@.40 <NO+ 6Z. @H >r&' +T+7 /-+7 6.3& >5 $i+6d &7p& $3. 67H&7 '7-
1*&/@.40 $3 67H&7 '7- /?4B
;TBF!O4!B5 Q7T6 7-?& 1H- ,3 4Z+7 ,.'-+ <NO+ 67-S6 LS 1H. +7. <hK @H +GH &9 ,3 ! L7- $3
+7• L7- 1*&/@.40 6@.&' 67H&7 '7- 1*&/@.40 6Nd&' :&' $P- $i+6d 1H- +9 67[ 1vH <NO+ 456
,g- 6Z- >-6 >p+ +H. &7b6 l
&Y!
B D. <9 &SK >-6 ! lKb6 7-?& w <hK @H +GH 4Z+7 Q7T6 7-?& 1H- 67D
>-6 &7p& <NO+ ,3 >-6 1H- Q7e- 1vHf &SK >-6 k lKb6 7-?& 67D >-6 &7p& <NO+ ,3 <U&' ,3 L7A&'
Q7e- 1vHB
;TBF!M4! B-6 <hK 6-C& <NO+ /F+7 @H L7q- 67H&7 '7- <?4B )ï&' ,U+ <9 67H&7 '7-
1*&/@.40 +J&' /F+7 456 >-6B aSK LV 7-?K $IH <8+ @H ,3 1H- 67D 1Ï <NO+ 1vH $3 w <hK @H 1Ï
&7p& <NO+ LV 7-?K <U&'B xhK @H w 4Z+7 Q7T6 7-?& 1H- +J&' <NO+ 4~+ 7_- 6-SQ $3. 67H&7
'7- 1*&/@.40B uS6 RKe +9 456 1*&/@.40 6Nd&' :&' $P- $i+6d &7p& <# /F+7 $c >C& Q7e-B
;TBF!P4!s*&/@.40 4P- &7p& <NO+ w >NP+ y 1Ï /ï&' <[ Q7T6 7-?& 1H- w LV 7-?K LS 6-SQ
1~Q <NO+ <8+ @H L7q- 67H&7 '7- <?4B "Z+7 '-e- 4# ,=Q ,Z- w >NP+ z $3 yB
;TBF!Q4!"Z+7 '-e- 4# 1Ï '-e- 4# ,h& ,NO6 6I&' LV 7-?K 670. +T+7 6@C& +7. <S& L7- 6.3&
>5 $i+6d &7p& @ <NO+ <8+ @H L7q- 67H&7 '7- <?4B sHK L7- 6.3& >5 $i+6d @ <8+ @H L7q- 67H&7
'7- <?4X &SK 67H&7 '7- 1*&/@.40 +7:H 6.3& k &'7ÜH ,3 $i+6d ,g- <NO+ Q7T6 7-?& $3 1vH
<U&'B
)æ&'!


)æ&'z

T7H&7
'7- 1*&/@.40

T7H&7 '7- /?4

)æ&'

0
-

oi+6d
<NO+
1vH
1H-
)æ&'

@
!

)æ&'!

T7H&7
'7- 1*&/@.40

)7•&7 1*&/@.40

M· vßng
Hoµng ChiÕn Th¾ng

!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
!k

78!9:4 )7. 4# $%&' (7f {2 $P- 4H 6@p& 1-&7 '(l2 j ! n l n l
y
B "# &3* +9 L7.e&' +T+7
HH44-&' &7q &7b6 ,3 y $3 /. $p* +9 L7e &¨&' 1vH ,g- <d&B
G-e 1v +7Kg- &7p& @(l2 j @
k
n @
!
l n @
z
l
z
n @
y
l
y
n @
{
l
{
n @
|
l
|
n @
}
l

}
<NO+ /F+7 $3. 67H&7
'7- 1*&/@.40 6I 1H&' 6@T-B Be&' $i+6d ,g- $3 +T+ 1*&/@.40 6Nd&' :&' +GH +7U&' <NO+ LC w
>e&' zX
oi+6d ,g-
0(l2
s*&/@.40
1(l2
oi+6d 1*&/@.40
(1
kf
1
!
f 1
z
2
0
}
(l2 j l
}

0
|
(l2 j l
|

0
{
(l2 j l
{


0
y
(l2 j l
y

0
z
(l2 j l
z

0
!
(l2 j l
!

0
k
(l2 j l
k

1(l2 j ! n l
z

1(l2 j ! n l n l
z

1(l2 j l n l
z


1(l2 j ! n l
1(l2 j l
z

1(l2 j l
1(l2 j !
!k!
!!!
k!!
!!k
kk!
k!k
!kk
!
;</+!O4!7bF!Dg!3d*!@\!F)F!G-/9`X1h!DTg/+!E/+!@B*!C2!D(EF!/(i/!CTeF!F(,-_/!@\X!
D(2/(!+(*!G-/9`X1h!Dj!D`)*!G2/+!k(<*l!
s*&/@.40 1(l2 <NO+ 6E&7 >r&' +T+7 ,b* Q7h& /N +eK Q7iQ +7-H l
-
+7. '(l2B TI <9 1K*
@H $i+6d 1*&/@.40 6Nd&' :&'B
G-e 1v @r&' 456 ,g- <d& lKb6 7-?& w $F 6@E l
-
B sHK L7- +7Kg- &7pQ <NO+ /F+ $3. 67H&7 '7-
1*&/@.40B s*&/@.40 6@.&' /H&7 1T+7 '7- 1Ï ,3 (!k!2B TK* &7-C& 1HK (}Y-2 ,h& /F+7 67D &5-
/K&' +GH 67H&7 '7- L7A&' Q7e- ,3 (!k!2B oD 67S +h& 1vH ,g- 1*&/@.40 (!k!2B "56 4Z+7 '-e-
4# 7.3& +7•&7 <NO+ $Ï &7N 7D&7 }X
Mã vòng
Hoàng Chiến Thắng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
!!














Hình 6:!"Z+7 '-e- 4# +7. 4# $%&' (7f{2 $P- <H 67:+ 1-&7 +HIJ!K!=!L!I!L!I
O
!
>*.,!D<!m,)!D`n/(!+*<*!1?!/(T!G2,4!
G-e 1v $i+6d 4# $ j (!kk!k!!2 <NO+ 6@K*c& 673&7 $i+6d &7p& @ j (!k!!k!!2B "g- ,g-
<d& lKb6 7-?& w $F 6@E l
z
B u7- &7pQ <NO+ /F+7 $3. 67H&7 '7- <?4 $3 67H&7 '7- 1*&/@.40B
T7H&7 '7- 1*&/@.40 +7:H '-T 6@F (kk!2B p 7D&7 /NP- <W* ,3 4A 6e RKT 6@D&7 '7- /F+7 6@C& +T+
67H&7 '7- <?4 $3 67H&7 '7- 1*&/@.40B sHK { ,h& /F+7 &5- /K&' +GH 67H&7 '7- 1*&/@.40 ,3
(!k!2 $3 4ẫK ,g- @
z
1ẽ ,3 1m LS 6-SQ lKb6 L7q- 67H&7 '7- <?4B a7NO+ <-[4 +GH 4Z+7 '-e- 4#
7D&7 } ,3 67^- '-H& '-e- 4# ,WK /. Q7e- /F+7 $%&' 6I&' >-6 456B
B5 '-e- 4# &7N 6@C& <NO+ '8- ,3 >5 '-e- 4# "0''-6B ở >5 '-e- 4# &3* 6I 4# <NO+ <NH
$3. $F 6@E >p+ +H. &7b6 <S& $F 6@E 67bQ &7b6 $3 L7- /F+7 $%&' +e 67H&7 '7- <?4 $3 67H&7 '7-
1*&/@.40 <Cù /F+7 $%&' 1H&' Q7e-X B5 '-e- 4# "0''-6 +J&' +9 67[ '-e- 4# &'NO+f &'7ĩH ,3

&9 1ẽ '-e- 4# 6I $F 6@E >p+ 67bQ &7b6 <S& >p+ +H. &7b6B u7- <9f 67H&7 '7- <?4 $3 67H&7 '7-
1*&/@.40 1ẽ /F+7 1H&' 6@T-B

B5 /_& LC&7

)ổ&'

xhK @H
@(l2
)ổ&'

)ổ&'




xhK
$3.
M· vßng
Hoµng ChiÕn Th¾ng
!"#$%&'!%()*!'+, /!!!!!!!!!!!!!!!!!!!012*34!
!z

QKT 6@D&7 1vH 1H- +GH 4Z+7 <NO+ 4A 6e &7N 6@C& 7D&7 $Ï /Nì- <W*X


























oc &'K*C& 6~+f Q7Nd&' Q7TQ '-e- 4# "0''-6 +9 67[ TQ /;&' $P- >b6 LM 4# &3.f &7N&'
6@.&' 67\+ 6S 4Z+7 '-e- 4# @b6 Q7:+ 6ZQ $D $p* +%& &7-cK Q7Nd&' Q7TQ '-e- 4# L7T+ <#
<NO+ Q7T6 4-&7f +7U&' ,3 +T+ /Z&' >-S& 67[ 6I Q7Nd&' Q7TQ '-e- 4# "0''-6 &7N ,3X '-e- 4#
>r&' Q7Nd&' Q7TQ >É* ,g-f Q7Nd&' Q7TQ '-e- 4# >É* ,g- +e- 6-S&BBB 6KM 670. 6I&' 6@N^&' 7OQ
+; 67[ 43 +9 67[ 1v /;&' 456 4Z+7 '-e- 4# 7.=+ LS6 7OQ &7-cK 4Z+7 '-e- 4# &7r4 <e4
>e. 6m6 *CK +hK +GH 6I&' &7-?4 $; <=6 @HB
k

k

!


!

k

!

!

k

!

!

B~6 <hK

k

!

k

k

!

!

k


!

!

k

!

k

k

!

!

!

!

!

k

!

!

k


Lh& /F+7
T7: z
k

!

!

!

k

!

!

!

k

!

!

Lh& /F+7
T7: y
k

!


k

!

!

k

!

!

!

k

!

Lh& /F+7
T7: {

k

k

k

k


k

!

k

!

!

!

k

Lh& /F+7
T7: |

k

k

k

k

k

k

!


k

!

!

!

Lh& /F+7
T7: }
k

k

k

k

!

k

k

!

k

!


!

Lh& /F+7
T7:7
k

Lh& /F+7
T7:!

Tài liệu bạn tìm kiếm đã sẵn sàng tải về

Tải bản đầy đủ ngay
×