{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 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 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; 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