{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
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"" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 
}{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 
2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Outpu
t" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }
1 3 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "This is a Maple 7 (tm) wor
ksheet." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 117 "Here we give an example for matrices C and B, and a
lso give an example for the vectors x, z, and xprime (x'= xprime)." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "w
ith(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected na
mes norm and trace have been redefined and unprotected\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 577 "W1 := (Matrix(13, 16,  [[1,1,1,1,1
,1,1,1,1,1,1,1,1,1,1,1],[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1],[0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,-1,0],[0,0,-1,0,0,0,0,0,0,0,0,0,0,-1,0,0],[0,0,0,-
1,0,0,0,0,0,0,0,0,0,1,1,1],[0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0],[0,0,0,
0,0,-1,0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,-1,0,0,0,0,1,0,1,0,1],[0,0,0,
0,0,0,0,-1,0,0,0,-1,0,-1,-1,-2],[0,0,0,0,0,0,0,0,-1,0,0,1,0,1,1,2],[0,
0,0,0,0,0,0,0,0,-1,0,-1,0,-1,0,-1],[0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,-1,-
1],[0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1]], datatype = anything, storag
e = rectangular, order = Fortran_order, shape = []));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#W1G-%'RTABLEG6+\"(7(>H%)anythingG%'MatrixG%,rec
tangularG%.Fortran_orderG7\"\"\"#;\"\"\"\"#8;F0\"#;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 22 "C:=convert(W1,matrix);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7/72\"\"\"F*F*F*F*F*F*F*F*F*F*F*F*F
*F*F*72!\"\"\"\"!F-F-F-F-F-F-F-F-F-F-F-F-F-F,72F-F,F-F-F-F-F-F-F-F-F-F
-F-F-F,F-72F-F-F,F-F-F-F-F-F-F-F-F-F-F,F-F-72F-F-F-F,F-F-F-F-F-F-F-F-F
-F*F*F*72F-F-F-F-F,F-F-F-F-F-F-F,F-F-F-F-72F-F-F-F-F-F,F-F-F-F-F-F*F-F
-F*F*72F-F-F-F-F-F-F,F-F-F-F-F*F-F*F-F*72F-F-F-F-F-F-F-F,F-F-F-F,F-F,F
,!\"#72F-F-F-F-F-F-F-F-F,F-F-F*F-F*F*\"\"#72F-F-F-F-F-F-F-F-F-F,F-F,F-
F,F-F,72F-F-F-F-F-F-F-F-F-F-F,F,F-F-F,F,72F-F-F-F-F-F-F-F-F-F-F-F-F,F,
F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 551 "BJ := Matrix(16, 13, [[1,0,1,1,4,1,4,4,3,1
,4,4,4],[1,1,0,4,1,4,1,3,4,4,1,3,3],[1,1,4,0,1,4,3,1,4,4,3,1,3],[1,4,1
,1,0,3,4,4,1,3,4,4,4],[1,1,4,4,3,0,1,1,4,4,3,3,1],[1,4,1,3,4,1,0,4,1,3
,4,4,4],[1,4,3,1,4,1,4,0,1,3,4,4,4],[1,3,4,4,1,4,1,1,0,4,3,3,3],[1,1,4
,4,3,4,3,3,4,0,1,1,1],[1,4,1,3,4,3,4,4,3,1,0,4,4],[1,4,3,1,4,3,4,4,3,1
,4,0,4],[1,3,4,4,1,4,3,3,4,4,1,1,3],[1,4,3,3,4,1,4,4,3,1,4,4,0],[1,3,4
,4,3,4,1,3,4,4,1,3,1],[1,3,4,4,3,4,3,1,4,4,3,1,1],[1,4,3,3,4,3,4,4,1,3
,4,4,4]], datatype = anything, storage = rectangular, order = Fortran_
order, shape = []);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#BJG-%'RTABLE
G6+\"))yh'=%)anythingG%'MatrixG%,rectangularG%.Fortran_orderG7\"\"\"#;
\"\"\"\"#;;F0\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "B:=con
vert (BJ,matrix);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6
#727/\"\"\"\"\"!F*F*\"\"%F*F,F,\"\"$F*F,F,F,7/F*F*F+F,F*F,F*F-F,F,F*F-
F-7/F*F*F,F+F*F,F-F*F,F,F-F*F-7/F*F,F*F*F+F-F,F,F*F-F,F,F,7/F*F*F,F,F-
F+F*F*F,F,F-F-F*7/F*F,F*F-F,F*F+F,F*F-F,F,F,7/F*F,F-F*F,F*F,F+F*F-F,F,
F,7/F*F-F,F,F*F,F*F*F+F,F-F-F-7/F*F*F,F,F-F,F-F-F,F+F*F*F*7/F*F,F*F-F,
F-F,F,F-F*F+F,F,7/F*F,F-F*F,F-F,F,F-F*F,F+F,7/F*F-F,F,F*F,F-F-F,F,F*F*
F-7/F*F,F-F-F,F*F,F,F-F*F,F,F+7/F*F-F,F,F-F,F*F-F,F,F*F-F*7/F*F-F,F,F-
F,F-F*F,F,F-F*F*7/F*F,F-F-F,F-F,F,F*F-F,F,F," }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 117 " Note, \+
that in the following matrix, in the diagonal everything is 1, and any
 other entry is 0 either mod 2 or mod 3." }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "multiply(B,C);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%'matrixG6#7272\"\"\"\"\"!F)!\"$F)F*F*!\"#F)F*F
*F+F*F+F+F*72F)F(F*F)F*F)F+F*F*F)F+F*F+F*F*F+72F)F*F(F)F*F+F)F*F*F+F)F
*F+F*F*F+72F*F)F)F(F+F*F*F)F+F*F*F)F*F+F+F*72F)F*F*F+F(F)F)F*F*F+F+F*F
)F*F*F+72F*F)F+F*F)F(F*F)F+F*F*F+F*F)F+F*72F*F+F)F*F)F*F(F)F+F*F*F+F*F
+F)F*72F+F*F*F)F*F)F)F(F*F+F+F*F+F*F*F)72F)F*F*F+F*F+F+F*F(F)F)F*F)F*F
*F+72F*F)F+F*F+F*F*F+F)F(F*F)F*F)F+F*72F*F+F)F*F+F*F*F+F)F*F(F)F*F+F)F
*72F+F*F*F)F*F+F+F*F*F)F)F(F+F*F*F)72F*F+F+F*F)F*F*F+F)F*F*F+F(F)F)F*7
2F+F*F*F+F*F)F+F*F*F)F+F*F)F(F*F)72F+F*F*F+F*F+F)F*F*F+F)F*F)F*F(F)72F
*F+F+F*F+F*F*F)F+F*F*F)F*F)F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }{TEXT -1 48 "Let x_1, x_2,...,x_16 be the bits to b
e encoded." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "x:=array(1..16);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"xG-%&arrayG6$;\"\"\"\"#;7\"" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 36 "The 13 coordinates of the encoded x:" }{MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 17 
"z:=multiply(x,B);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"zG-%'vectorG
6#7/,B&%\"xG6#\"\"\"F-&F+6#\"\"#F-&F+6#\"\"$F-&F+6#\"\"%F-&F+6#\"\"&F-
&F+6#\"\"'F-&F+6#\"\"(F-&F+6#\"\")F-&F+6#\"\"*F-&F+6#\"#5F-&F+6#\"#6F-
&F+6#\"#7F-&F+6#\"#8F-&F+6#\"#9F-&F+6#\"#:F-&F+6#\"#;F-,@F.F-F1F-*&F6F
-F4F-F-F7F-*&F6F-F:F-F-*&F6F-F=F-F-*&F3F-F@F-F-FCF-*&F6F-FFF-F-*&F6F-F
IF-F-*&F3F-FLF-F-*&F6F-FOF-F-*&F3F-FRF-F-*&F3F-FUF-F-*&F6F-FXF-F-,@F*F
-*&F6F-F1F-F-F4F-*&F6F-F7F-F-F:F-*&F3F-F=F-F-*&F6F-F@F-F-*&F6F-FCF-F-F
FF-*&F3F-FIF-F-*&F6F-FLF-F-*&F3F-FOF-F-*&F6F-FRF-F-*&F6F-FUF-F-*&F3F-F
XF-F-,@F*F-*&F6F-F.F-F-F4F-*&F6F-F7F-F-*&F3F-F:F-F-F=F-*&F6F-F@F-F-*&F
6F-FCF-F-*&F3F-FFF-F-FIF-*&F6F-FLF-F-*&F3F-FOF-F-*&F6F-FRF-F-*&F6F-FUF
-F-*&F3F-FXF-F-,@F*F6F.F-F1F-*&F3F-F7F-F-*&F6F-F:F-F-*&F6F-F=F-F-F@F-*
&F3F-FCF-F-*&F6F-FFF-F-*&F6F-FIF-F-FLF-*&F6F-FOF-F-*&F3F-FRF-F-*&F3F-F
UF-F-*&F6F-FXF-F-,@F*F-*&F6F-F.F-F-*&F6F-F1F-F-*&F3F-F4F-F-F:F-F=F-*&F
6F-F@F-F-*&F6F-FCF-F-*&F3F-FFF-F-*&F3F-FIF-F-*&F6F-FLF-F-FOF-*&F6F-FRF
-F-*&F6F-FUF-F-*&F3F-FXF-F-,@F*F6F.F-*&F3F-F1F-F-*&F6F-F4F-F-F7F-*&F6F
-F=F-F-F@F-*&F3F-FCF-F-*&F6F-FFF-F-*&F6F-FIF-F-*&F3F-FLF-F-*&F6F-FOF-F
-FRF-*&F3F-FUF-F-*&F6F-FXF-F-,@F*F6*&F3F-F.F-F-F1F-*&F6F-F4F-F-F7F-*&F
6F-F:F-F-F@F-*&F3F-FCF-F-*&F6F-FFF-F-*&F6F-FIF-F-*&F3F-FLF-F-*&F6F-FOF
-F-*&F3F-FRF-F-FUF-*&F6F-FXF-F-,@F*F3*&F6F-F.F-F-*&F6F-F1F-F-F4F-*&F6F
-F7F-F-F:F-F=F-*&F6F-FCF-F-*&F3F-FFF-F-*&F3F-FIF-F-*&F6F-FLF-F-*&F3F-F
OF-F-*&F6F-FRF-F-*&F6F-FUF-F-FXF-,@F*F-*&F6F-F.F-F-*&F6F-F1F-F-*&F3F-F
4F-F-*&F6F-F7F-F-*&F3F-F:F-F-*&F3F-F=F-F-*&F6F-F@F-F-FFF-FIF-*&F6F-FLF
-F-FOF-*&F6F-FRF-F-*&F6F-FUF-F-*&F3F-FXF-F-,@F*F6F.F-*&F3F-F1F-F-*&F6F
-F4F-F-*&F3F-F7F-F-*&F6F-F:F-F-*&F6F-F=F-F-*&F3F-F@F-F-FCF-*&F6F-FIF-F
-FLF-*&F6F-FOF-F-FRF-*&F3F-FUF-F-*&F6F-FXF-F-,@F*F6*&F3F-F.F-F-F1F-*&F
6F-F4F-F-*&F3F-F7F-F-*&F6F-F:F-F-*&F6F-F=F-F-*&F3F-F@F-F-FCF-*&F6F-FFF
-F-FLF-*&F6F-FOF-F-*&F3F-FRF-F-FUF-*&F6F-FXF-F-,@F*F6*&F3F-F.F-F-*&F3F
-F1F-F-*&F6F-F4F-F-F7F-*&F6F-F:F-F-*&F6F-F=F-F-*&F3F-F@F-F-FCF-*&F6F-F
FF-F-*&F6F-FIF-F-*&F3F-FLF-F-FRF-FUF-*&F6F-FXF-F-" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 161 "y is the decoded vector wit
h 16 coordinates; note that in its i-th coordinate, only x_i has coeff
icient 1, any other x_j has coefficient 0 either mod 2 or mod 3." }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "xprime:
=multiply(z,C);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'xprimeG-%'vector
G6#72,:&%\"xG6#\"\"\"F-*&\"\"$F-&F+6#\"\"%F-!\"\"*&F/F-&F+6#\"\"'F-F3*
&F/F-&F+6#\"\"(F-F3*&\"\"#F-&F+6#\"\")F-F3*&F/F-&F+6#\"#5F-F3*&F/F-&F+
6#\"#6F-F3*&F=F-&F+6#\"#7F-F3*&F/F-&F+6#\"#8F-F3*&F=F-&F+6#\"#9F-F3*&F
=F-&F+6#\"#:F-F3*&F/F-&F+6#\"#;F-F3,:&F+6#F=F-*&F/F-&F+6#F/F-F3*&F/F-&
F+6#\"\"&F-F3*&F=F-F9F-F3*&F/F-F>F-F3*&F/F-&F+6#\"\"*F-F3*&F=F-FFF-F3*
&F/F-FJF-F3*&F=F-FNF-F3*&F/F-FRF-F3*&F/F-FVF-F3*&F=F-FZF-F3,:Fhn!\"$F[
oF-*&F/F-F^oF-F3*&F=F-F5F-F3*&F/F-F>F-F3*&F/F-FdoF-F3*&F=F-FBF-F3*&F/F
-FJF-F3*&F=F-FNF-F3*&F/F-FRF-F3*&F/F-FVF-F3*&F=F-FZF-F3,:F*F^pF0F-*&F=
F-F^oF-F3*&F/F-F5F-F3*&F/F-F9F-F3*&F=F-FdoF-F3*&F/F-FBF-F3*&F/F-FFF-F3
*&F/F-FNF-F3*&F=F-FRF-F3*&F=F-FVF-F3*&F/F-FZF-F3,:FhnF^p*&F/F-F[oF-F3*
&F=F-F0F-F3F^oF-*&F/F-F>F-F3*&F/F-FdoF-F3*&F=F-FBF-F3*&F=F-FFF-F3*&F/F
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0F-F3F5F-*&F/F-F9F-F3*&F=F-FdoF-F3*&F/F-FBF-F3*&F/F-FFF-F3*&F=F-FJF-F3
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F/F-F5F-F3F9F-*&F=F-FdoF-F3*&F/F-FBF-F3*&F/F-FFF-F3*&F=F-FJF-F3*&F/F-F
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F-FVF-F3*&F=F-FZF-F3,:F*F^p*&F=F-F[oF-F3*&F/F-F0F-F3*&F=F-F^oF-F3*&F/F
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M7R0
I4RTABLE_SAVE/2919712X,%)anythingG6"6"[gl!"%!!!#[x"."1"""!""""!F)F)F)F)F)F)F)F)
F)F)F'F)F(F)F)F)F)F)F)F)F)F)F)F'F)F)F(F)F)F)F)F)F)F)F)F)F'F)F)F)F(F)F)F)F)F)F)F
)F)F'F)F)F)F)F(F)F)F)F)F)F)F)F'F)F)F)F)F)F(F)F)F)F)F)F)F'F)F)F)F)F)F)F(F)F)F)F)
F)F'F)F)F)F)F)F)F)F(F)F)F)F)F'F)F)F)F)F)F)F)F)F(F)F)F)F'F)F)F)F)F)F)F)F)F)F(F)F
)F'F)F)F)F)F)F)F)F)F)F)F(F)F'F)F)F)F)F(F'F'F(F'F(F(F)F'F)F)F)F)F)F)F)F)F)F)F)F(
F'F)F)F(F'F)F)F'F(F'F(F)F(F'F)F(F)F'F)F'F)F(F'F)F(F(F'F(F)F)F'F)F'F'!"#""#F(F(F
(6"
}
{RTABLE 
M7R0
I5RTABLE_SAVE/18661788X,%)anythingG6"6"[gl!"%!!!#[x"1"."""F'F'F'F'F'F'F'F'F'F'F
'F'F'F'F'""!F'F'""%F'F)F)""$F'F)F)F*F)F*F*F)F'F(F)F'F)F'F*F)F)F'F*F)F*F)F)F*F'F
)F(F'F)F*F'F)F)F*F'F)F*F)F)F*F)F'F'F(F*F)F)F'F*F)F)F'F)F*F*F)F'F)F)F*F(F'F'F)F)
F*F*F)F'F)F)F*F)F'F*F)F'F(F)F'F*F)F)F*F)F'F*F)F)F*F'F)F'F)F(F'F*F)F)F*F)F*F'F)F
*F)F)F'F)F'F'F(F)F*F*F)F*F)F)F'F'F)F)F*F)F*F*F)F(F'F'F)F'F)F)F*F)F'F*F)F*F)F)F*
F'F(F)F'F)F'F*F)F)F*F'F)F*F)F)F*F'F)F(F'F)F*F'F)F)F*F*F)F'F)F)F*F'F)F)F*F(F'F'F
)6"
}