{VERSION 5 0 "APPLE_PPC_MAC" "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" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "p := x -> x^5 + x^3 + 1:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "Primitive(p(x)) mod 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f s := 2^(degree(p(x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fsG\"#K" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "field := vector(fs);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&fieldG-%&arrayG6$;\"\"\"\"#K7\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "for i from 1 to fs-1 do" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " field[i] := Powmod(a, i, p(a), \+ a) mod 2:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "field[fs] := 0:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "evalm(field);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-% 'vectorG6#7B%\"aG*$)F'\"\"#\"\"\"*$)F'\"\"$F+*$)F'\"\"%F+,&F,F+F+F+,&F /F+F'F+,(F,F+F(F+F+F+,(F/F+F,F+F'F+,*F/F+F,F+F(F+F+F+,(F/F+F'F+F+F+,*F ,F+F(F+F'F+F+F+,*F/F+F,F+F(F+F'F+,(F/F+F(F+F+F+,&F'F+F+F+,&F(F+F'F+,&F ,F+F(F+,&F/F+F,F+,(F/F+F,F+F+F+,*F/F+F,F+F'F+F+F+,,F/F+F,F+F(F+F'F+F+F +,*F/F+F(F+F'F+F+F+,(F(F+F'F+F+F+,(F,F+F(F+F'F+,(F/F+F,F+F(F+,&F/F+F+F +,(F,F+F'F+F+F+,(F/F+F(F+F'F+,&F(F+F+F+,&F,F+F'F+,&F/F+F(F+F+\"\"!" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "ftable := table():" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "for i from 1 to fs-1 do" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " ftable[ field[i] ] := a^i:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ftable[ field[fs] ] := 0:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 7 "t := 4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "g := product(x-a^j, j=1..2*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"gG*2,&%\"xG\"\"\"%\"aG!\"\"F(,&F'F(*$)F)\"\"#F(F*F(,&F'F(*$)F)\"\" $F(F*F(,&F'F(*$)F)\"\"%F(F*F(,&F'F(*$)F)\"\"&F(F*F(,&F'F(*$)F)\"\"'F(F *F(,&F'F(*$)F)\"\"(F(F*F(,&F'F(*$)F)\"\")F(F*F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 806 "rscoeff := proc(f, x, p, a)\n local g, i, \+ j, ng, cg, fs, field, ftable;\n fs := 2^(degree(p));\n field := \+ linalg[vector](fs);\n for i from 1 to fs-1 do\n field[i] := \+ Powmod(a, i, p, a) mod 2:\n od:\n field[fs] := 0;\n ftable := table();\n for i from 1 to fs-1 do\n ftable[ field[i] ] := \+ a^i:\n od:\n ftable[ field[fs] ] := 0;\n g := expand(f) mod 2 ;\n ng := 0;\n for j from 0 to degree(g,x) do\n cg := coe ff(g, x, j):\n cg := ftable[ Rem(numer(cg), p, a) mod 2 ]\n \+ / ftable[ Rem(denom(cg), p, a) mod 2 ];\n if degree(c g,a) < 0 then\n cg := cg * a^(fs-1);\n fi:\n i f degree(cg,a) = (fs-1) then\n cg := cg/a^(fs-1);\n f i:\n ng := ng + cg*x^j:\n od:\n g := sort(ng mod 2, x);\n RETURN(g);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "g : = rscoeff(g, x, p(a), a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,4* $)%\"xG\"\")\"\"\"F**&)%\"aG\"\"'F*)F(\"\"(F*F**&)F-\"#FF*)F(F.F*F**&) F-\"\"%F*)F(\"\"&F*F**&)F-\"# " 0 "" {MPLTEXT 1 0 93 "b := a^18*x^8 + a^20*x^7 + a^19*x^6 + a^23*x^5 + a^6*x^4 + a^2*x^3 + a^23*x^2 + a^4*x + a^15:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "c := rscoeff(b*g, x, p(a), a);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"cG,B*&)%\"aG\"#=\"\"\")%\"xG\"#;F*F**&)F(\"#9F*) F,\"#:F*F**&)F(\"#5F*)F,F0F*F**&)F(\"#IF*)F,\"#8F*F**&)F(\"\"'F*)F,\"# 7F*F**&)F(\"#CF*)F,\"#6F*F**&)F(\"\"&F*)F,F5F*F**&)F(\"#EF*)F,\"\"*F*F **&)F(\"#FF*)F,\"\")F*F**&F8F*)F,\"\"(F*F**&FBF*)F,F>F*F**&FPF*)F,FHF* F**&)F(\"#@F*)F,\"\"%F*F**&)F(FNF*)F,\"\"#F*F**&)F(\"#GF*F,F*F**$)F(\" #?F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 597 "binmess := proc( cw, n, p, a, ml)\n local i, j, bvect, vs, pco, dga, binmat, binvect ;\n for i from 0 to ml do\n pco := coeff(cw, x, i):\n \+ if pco <> 0 then\n dga := degree(pco, a):\n pco : = Powmod(a, dga, p, a) mod 2:\n fi:\n vs := []:\n \+ for j from 0 to n-1 do\n vs := [op(vs), coeff(pco, a, j)]: \n od:\n if i = 0 then\n binmat := linalg[matr ix](1, n, vs):\n else\n binmat := linalg[stackmatrix] (binmat, vs):\n fi:\n od:\n binvect := convert(binmat, ve ctor);\n RETURN(evalm(binvect));\nend:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 48 "cbin := binmess(c, degree(p(x)), p(a), a, fs-2);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%cbinG-%'vectorG6#7gt\"\"\"F)F)F)F) F)\"\"!F)F*F*F)F*F)F)F)F*F*F*F*F*F)F)F)F*F)F*F)F)F*F)F*F*F)F)F)F*F*F)F *F)F*F)F)F*F)F)F)F*F)F*F)F*F*F)F*F*F*F)F)F)F*F)F*F*F)F*F*F)F*F)F)F)F*F *F)F)F)F*F*F*F)F*F*F)F)F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F *F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F *F*F*F*F*F*F*F*F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 482 "rbin := vector([1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, \+ 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0 , 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, \+ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 380 "bincoeff := proc(n, bmess) \n local i, j, k, bk, pcoeff, poly;\n pcoeff := []:\n bk := l inalg[vectdim](bmess);\n i := 0;\n k := 0;\n while i < bk do \n poly := 0:\n for j from 1 to n do\n poly : = poly + bmess[i+j]*a^(j-1):\n od:\n pcoeff := [op(pcoef f), poly]:\n k := k+1;\n i := k*n;\n od:\n RETURN( evalm(pcoeff)):\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "pc oeff := bincoeff(5, rbin);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'pcoef fG-%'vectorG6#7A,,*$)%\"aG\"\"%\"\"\"F.*$)F,\"\"$F.F.*$)F,\"\"#F.F.F,F .F.F.,&F2F.F.F.,*F*F.F/F.F2F.F.F.\"\"!,*F*F.F2F.F,F.F.F.,(F*F.F2F.F,F. ,(F*F.F/F.F2F.,&F*F.F2F.F9,*F*F.F/F.F,F.F.F.,&F/F.F2F.,&F/F.F,F.,(F/F. F,F.F.F.F)F*,(F/F.F2F.F.F.,(F*F.F,F.F.F.F=,&F*F.F/F.,(F*F.F/F.F.F.F8FB FCF7F7F7F7F7F7F7F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "r := \+ sum('pcoeff[i]*x^(i-1)', 'i'=1..vectdim(pcoeff));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"rG,V\"\"\"F&%\"aGF&*$)F'\"\"$F&F&*&,&*$)F'\"\"#F&F& F&F&F&%\"xGF&F&*&,**$)F'\"\"%F&F&F(F&F-F&F&F&F&)F0F/F&F&*&,*F3F&F-F&F' F&F&F&F&)F0F5F&F&*&,(F3F&F-F&F'F&F&)F0\"\"&F&F&*&,(F3F&F(F&F-F&F&)F0\" \"'F&F&*&,&F3F&F-F&F&)F0\"\"(F&F&*&F;F&)F0\"\")F&F&*&,*F3F&F(F&F'F&F&F &F&)F0\"\"*F&F&*&,&F(F&F-F&F&)F0\"#5F&F&*&,&F(F&F'F&F&)F0\"#6F&F&*&,(F (F&F'F&F&F&F&)F0\"#7F&F&*&,,F3F&F(F&F-F&F'F&F&F&F&)F0\"#8F&F&*&F4F&)F0 \"#9F&F&*&,(F(F&F-F&F&F&F&)F0\"#:F&F&*&,(F3F&F'F&F&F&F&)F0\"#;F&F&*&FN F&)F0\"#F&F&*&F 8F&)F0\"#?F&F&*&FfoF&)F0\"#@F&F&*&FjoF&)F0\"#AF&F&F-F&F3F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "r := rscoeff(r, x, p(a), a);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"rG,N*&)%\"aG\"#=\"\"\")%\"xG\"#AF* F**&)F(\"#F*F**&F/F*)F, F)F*F**&)F(\"#;F*)F,F0F*F**&)F(\"#5F*)F,F>F*F**&)F(\"\"(F*)F,\"#:F*F** &)F(\"\"%F*)F,\"#9F*F**&)F(F6F*)F,\"#8F*F**&)F(\"#EF*)F,\"#7F*F**&)F( \"#HF*)F,\"#6F*F**&F=F*)F,FBF*F**&)F(F9F*)F,\"\"*F*F**&)F(\"#FF*)F,\" \")F*F**&)F(\"#IF*)F,FFF*F**&)F(\"#CF*)F,\"\"'F*F**&F]oF*)F,\"\"&F*F** &F4F*)F,FKF*F**&)F(F[oF*)F,\"\"#F*F**&)F(\"#GF*F,F*F**$FOF*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "r := unapply(r, x);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"rGf*6#%\"xG6\"6$%)operatorG%&arrow GF(,N*&)%\"aG\"#=\"\"\")9$\"#AF1F1*&)F/\"#F1F1*&F6F1)F3F0F1F1*&)F/\"#;F1)F3F7F1F1*&)F/\"#5F1) F3FEF1F1*&)F/\"\"(F1)F3\"#:F1F1*&)F/\"\"%F1)F3\"#9F1F1*&)F/F=F1)F3\"#8 F1F1*&)F/\"#EF1)F3\"#7F1F1*&)F/\"#HF1)F3\"#6F1F1*&FDF1)F3FIF1F1*&)F/F@ F1)F3\"\"*F1F1*&)F/\"#FF1)F3\"\")F1F1*&)F/\"#IF1)F3FMF1F1*&)F/\"#CF1)F 3\"\"'F1F1*&FdoF1)F3\"\"&F1F1*&F;F1)F3FRF1F1*&)F/FboF1)F3\"\"#F1F1*&)F /\"#GF1F3F1F1*$FVF1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Sa := vector(2*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#SaG-%&arr ayG6$;\"\"\"\"\")7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for i from 1 to 2*t do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " Sa[i] := ftable[ Rem(r(a^i), p(a), a) mod 2 ];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " if degree(Sa[i], a) = (fs-1) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " Sa[i] := Sa[i]/a^(fs-1):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalm(Sa);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7**$)%\"aG\"#8\"\"\"*$)F)\"#?F+*$)F)\"\" )F+*$)F)\"\"#F+*$)F)\"#@F+*$)F)\"#9F+*$)F)\"\"$F+F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "S := sum('Sa[j+1]*z^j', 'j'=0..2*t-1);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG,2*$)%\"aG\"#8\"\"\"F**&)F(\"#? F*%\"zGF*F**&)F(\"\")F*)F.\"\"#F*F**&)F(F3F*)F.\"\"$F*F**&)F(\"#@F*)F. \"\"%F*F**&)F(\"#9F*)F.\"\"&F*F**&)F(F7F*)F.\"\"'F*F**&FCF*)F.\"\"(F*F *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "S := unapply(S, z);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SGf*6#%\"zG6\"6$%)operatorG%&arro wGF(,2*$)%\"aG\"#8\"\"\"F1*&)F/\"#?F19$F1F1*&)F/\"\")F1)F5\"\"#F1F1*&) F/F:F1)F5\"\"$F1F1*&)F/\"#@F1)F5\"\"%F1F1*&)F/\"#9F1)F5\"\"&F1F1*&)F/F >F1)F5\"\"'F1F1*&FJF1)F5\"\"(F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f := z^(2*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" fG*$)%\"zG\"\")\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 764 "r seuclid := proc(t, f, g, z, p, a)\n local q, r, rm1, rp1, um1, u, u p1, vm1, v, vp1, i;\n rm1 := sort(Expand(f) mod 2);\n r := sort( Expand(g) mod 2);\n um1 := 1;\n u := 0;\n vm1 := 0;\n v := 1;\n while degree(r,z) >= t do\n rp1 := Rem(rm1, r, z, 'q') mod 2;\n rp1 := rscoeff(rp1, z, p, a);\n q := rscoeff(q , z, p, a);\n vp1 := expand(vm1 - v*q) mod 2;\n vm1 := v ;\n v := sort(vp1, z);\n v := rscoeff(v, z, p, a);\n \+ up1 := expand(um1 - u*q) mod 2;\n um1 := u;\n u := s ort(up1);\n u := rscoeff(u, z, p, a);\n rm1 := r;\n \+ r := sort(rp1, z);\n print(`Q = `, q, ` R = `, r, \n \+ ` V = `, v, ` U = `, u);\n od;\n print();\n RETUR N(q, r, v, u):\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "res := rseuclid(t, f, S(z), z, p(a), a);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6*%%Q~=~G,&*&)%\"aG\"#G\"\"\"%\"zGF)F)*$F&F)F)%(~~~R~=~G,0*&)F'\"#BF) )F*\"\"'F)F)*&)F'\"#FF))F*\"\"&F)F)*&)F'\"\"(F))F*\"\"%F)F)*&)F'\"\"*F ))F*\"\"$F)F)*&)F'\"#DF))F*\"\"#F)F)*&)F'\"#EF)F*F)F)*$)F'\"#5F)F)%(~~ ~V~=~GF$%(~~~U~=~GF)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6*%%Q~=~G,&*&)% \"aG\"#6\"\"\"%\"zGF)F)*$)F'\"\"&F)F)%(~~~R~=~G,.*&)F'\"#%$resG6&,&*&)%\"aG\"#A\"\"\"%\"zGF+F+*$)F)\"\")F+F+,** &)F)\"#CF+)F,\"\"$F+F+*&)F)\"\"(F+)F,\"\"#F+F+*&)F)\"#;F+F,F+F+*$F(F+F +,,*&)F)\"\"&F+)F,\"\"%F+F+*$F4F+F+*&F2F+F9F+F+*&)F)F:F+F,F+F+*$)F)\" \"*F+F+,**&F.F+F4F+F+*&)F)\"\"'F+F9F+F+*&)F)\"#GF+F,F+F+*$)F)\"#@F+F+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "R := res[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG,**&)%\"aG\"#C\"\"\")%\"zG\"\"$F*F**&) F(\"\"(F*)F,\"\"#F*F**&)F(\"#;F*F,F*F**$)F(\"#AF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "R := unapply(R, z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RGf*6#%\"zG6\"6$%)operatorG%&arrowGF(,**&)%\"aG\"#C \"\"\")9$\"\"$F1F1*&)F/\"\"(F1)F3\"\"#F1F1*&)F/\"#;F1F3F1F1*$)F/\"#AF1 F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "V := res[3];" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG,,*&)%\"aG\"\"&\"\"\")%\"zG\"\" %F*F**$)F,\"\"$F*F**&)F(\"#CF*)F,\"\"#F*F**&)F(F5F*F,F*F**$)F(\"\"*F*F *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "V := unapply(V, z);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VGf*6#%\"zG6\"6$%)operatorG%&arro wGF(,,*&)%\"aG\"\"&\"\"\")9$\"\"%F1F1*$)F3\"\"$F1F1*&)F/\"#CF1)F3\"\"# F1F1*&)F/F " 0 "" {MPLTEXT 1 0 23 "for i from 1 to fs-1 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " if (Rem(V(a^i), p(a), a) mod 2) = 0 then" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 " print(a^i, ` is a root o f `, V(z), ` error position is `, degree(a^(fs-1)/a^i, a));" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'*$)%\"aG\"#:\" \"\"%5~~~~is~a~root~of~~~~G,,*&)F%\"\"&F')%\"zG\"\"%F'F'*$)F.\"\"$F'F' *&)F%\"#CF')F.\"\"#F'F'*&)F%F7F'F.F'F'*$)F%\"\"*F'F'%8~~~error~positio n~is~~~G\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'*$)%\"aG\"#;\"\"\"%5~~ ~~is~a~root~of~~~~G,,*&)F%\"\"&F')%\"zG\"\"%F'F'*$)F.\"\"$F'F'*&)F%\"# CF')F.\"\"#F'F'*&)F%F7F'F.F'F'*$)F%\"\"*F'F'%8~~~error~position~is~~~G \"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'*$)%\"aG\"#<\"\"\"%5~~~~is~a~r oot~of~~~~G,,*&)F%\"\"&F')%\"zG\"\"%F'F'*$)F.\"\"$F'F'*&)F%\"#CF')F.\" \"#F'F'*&)F%F7F'F.F'F'*$)F%\"\"*F'F'%8~~~error~position~is~~~G\"#9" }} {PARA 11 "" 1 "" {XPPMATH 20 "6'*$)%\"aG\"#=\"\"\"%5~~~~is~a~root~of~~ ~~G,,*&)F%\"\"&F')%\"zG\"\"%F'F'*$)F.\"\"$F'F'*&)F%\"#CF')F.\"\"#F'F'* &)F%F7F'F.F'F'*$)F%\"\"*F'F'%8~~~error~position~is~~~G\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Vp := diff(V(z), z) mod 2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#VpG,&*$)%\"zG\"\"#\"\"\"F**$)%\"aGF )F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Vp := unapply(Vp, \+ z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#VpGf*6#%\"zG6\"6$%)operatorG %&arrowGF(,&*$)9$\"\"#\"\"\"F1*$)%\"aGF0F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "e13 := ftable[ Rem(R(a^18), p(a), a) mod 2 \+ ] / ftable[ Rem(Vp(a^18), p(a), a) mod 2 ]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "e14 := ftable[ Rem(R(a^17), p(a), a) mod 2 ] / fta ble[ Rem(Vp(a^17), p(a), a) mod 2 ]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "e15 := ftable[ Rem(R(a^16), p(a), a) mod 2 ] / ftable [ Rem(Vp(a^16), p(a), a) mod 2 ]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "e16 := ftable[ Rem(R(a^15), p(a), a) mod 2 ] / ftable [ Rem(Vp(a^15), p(a), a) mod 2 ]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "e := e16*x^16 + e15*x^15 + e14*x^14 + e13*x^13;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG,**&)%\"aG\"#9\"\"\")%\"xG\"#;F* F**&F(F*)F,\"#:F*F**&)F(\"#7F*)F,F)F*F**&)F(\"\"#F*)F,\"#8F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "e := unapply(rscoeff(e, x, p (a), a), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eGf*6#%\"xG6\"6$%) operatorG%&arrowGF(,**&)%\"aG\"#9\"\"\")9$\"#;F1F1*&F/F1)F3\"#:F1F1*&) F/\"#7F1)F3F0F1F1*&)F/\"\"#F1)F3\"#8F1F1F(F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 36 "c := rscoeff(r(x)+e(x), x, p(a), a);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"cG,N*&)%\"aG\"#=\"\"\")%\"xG\"#AF*F**&)F (\"#F*F**&F/F*)F,F)F*F* *&)F(\"#;F*)F,F0F*F**&)F(\"\"%F*)F,F>F*F**&)F(\"#6F*)F,\"#:F*F**&)F(\" #BF*)F,\"#9F*F**&)F(F9F*)F,\"#8F*F**&)F(\"#EF*)F,\"#7F*F**&)F(\"#HF*)F ,FFF*F**&F=F*)F,\"#5F*F**&FOF*)F,\"\"*F*F**&)F(\"#FF*)F,\"\")F*F**&)F( \"#IF*)F,\"\"(F*F**&)F(\"#CF*)F,\"\"'F*F**&F\\oF*)F,\"\"&F*F**&F4F*)F, FBF*F**&)F(FjnF*)F,\"\"#F*F**&)F(\"#GF*F,F*F**$)F(F6F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "seq(Rem(subs(x=a^i, c), p(a), a) mo d 2, i = 1..2*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6*\"\"!F#F#F#F#F#F# F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "ebin := binmess(e(x), degree(p(x)), p(a), a, fs-2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%e binG-%'vectorG6#7gt\"\"!F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F) F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F) F)F)F)F)F)F)F)F)\"\"\"F)F)F)F*F*F*F*F)F*F)F)F)F*F*F)F)F)F)F)F)F)F)F)F) F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F) F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "berrors := sum('ebin[i]', 'i'=1..ve ctdim(ebin));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(berrorsG\"\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 } {VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }