//     Table of polynomials
// 
//     How to read the table
// -----------------------------------------------------------------------------
// 
// This file contains a table of irreducible polynomials, one polynomial for
// each degree up to 4000. 
// The polynomials are found using Magma by a lexicographic search among the
// possible trinomials of the given degrees. 
// In case no irreducible trinomial is found for the given degree, 
// the search continues with pentanomials and so on.
// The first irreducible polynomial found using this procedure is choosen.
// The result is that the polynomial choosen has minimum possible weight for the
// given degree, $m$, and given that weight it has the minimum degree, $k_1$, of
// the second term and so on. 
// 
// To save space we have only listed the degrees of the mid terms, since
// irreducible polynomials always contain 1 and x^m, where m is the degree.
// The table should be interpreted as follows. 
// The polynomial is a trinomial if there is only one mid term, and it is a
// pentanomial if there are three mid terms.
// As an example, take the entries for degrees 90 and 91:
// 
//   90    27 
//   91    8, 5, 1 
// 
// This should be interpreted as the polynomials 
// 
//   x^90 + x^27 + 1
// 
// and 
// 
//   x^91 + x^8 + x^5 + x + 1
// 
// 
// -----------------------------------------------------------------------------
//     The table itself
// -----------------------------------------------------------------------------

print "Create PolynomialAlgebra P<x>";
P<x>:=PolynomialAlgebra(GF(2));

print "Define function PolynomialWeight";
function PolynomialWeight(fx); 
//-------------------------------------------------------------------
// PolynomialWeight takes a polynomial fx and extracts its weight,
// that is the number of nonzero components in fx.
// 
// Created by Mikael Olofsson 960612.
//-------------------------------------------------------------------
  if (Degree(fx) mod 200) eq 0 then
    print "  Done up to degree", Degree(fx);
  end if;
  A:=Coefficients(fx);
  while Position(A,0) ne 0 do
    Exclude(~A,0);
  end while;
  return #A;
end function;

print "Define sequence MinWeightPolynomials";
MinWeightPolynomials:=[
  x + 1,
  x^2 + x + 1,
  x^3 + x + 1,
  x^4 + x + 1,
  x^5 + x^2 + 1,
  x^6 + x + 1,
  x^7 + x + 1,
  x^8 + x^4 + x^3 + x + 1,
  x^9 + x + 1,
  x^10 + x^3 + 1,
  x^11 + x^2 + 1,
  x^12 + x^3 + 1,
  x^13 + x^4 + x^3 + x + 1,
  x^14 + x^5 + 1,
  x^15 + x + 1,
  x^16 + x^5 + x^3 + x + 1,
  x^17 + x^3 + 1,
  x^18 + x^3 + 1,
  x^19 + x^5 + x^2 + x + 1,
  x^20 + x^3 + 1,
  x^21 + x^2 + 1,
  x^22 + x + 1,
  x^23 + x^5 + 1,
  x^24 + x^4 + x^3 + x + 1,
  x^25 + x^3 + 1,
  x^26 + x^4 + x^3 + x + 1,
  x^27 + x^5 + x^2 + x + 1,
  x^28 + x + 1,
  x^29 + x^2 + 1,
  x^30 + x + 1,
  x^31 + x^3 + 1,
  x^32 + x^7 + x^3 + x^2 + 1,
  x^33 + x^10 + 1,
  x^34 + x^7 + 1,
  x^35 + x^2 + 1,
  x^36 + x^9 + 1,
  x^37 + x^6 + x^4 + x + 1,
  x^38 + x^6 + x^5 + x + 1,
  x^39 + x^4 + 1,
  x^40 + x^5 + x^4 + x^3 + 1,
  x^41 + x^3 + 1,
  x^42 + x^7 + 1,
  x^43 + x^6 + x^4 + x^3 + 1,
  x^44 + x^5 + 1,
  x^45 + x^4 + x^3 + x + 1,
  x^46 + x + 1,
  x^47 + x^5 + 1,
  x^48 + x^5 + x^3 + x^2 + 1,
  x^49 + x^9 + 1,
  x^50 + x^4 + x^3 + x^2 + 1,
  x^51 + x^6 + x^3 + x + 1,
  x^52 + x^3 + 1,
  x^53 + x^6 + x^2 + x + 1,
  x^54 + x^9 + 1,
  x^55 + x^7 + 1,
  x^56 + x^7 + x^4 + x^2 + 1,
  x^57 + x^4 + 1,
  x^58 + x^19 + 1,
  x^59 + x^7 + x^4 + x^2 + 1,
  x^60 + x + 1,
  x^61 + x^5 + x^2 + x + 1,
  x^62 + x^29 + 1,
  x^63 + x + 1,
  x^64 + x^4 + x^3 + x + 1,
  x^65 + x^18 + 1,
  x^66 + x^3 + 1,
  x^67 + x^5 + x^2 + x + 1,
  x^68 + x^9 + 1,
  x^69 + x^6 + x^5 + x^2 + 1,
  x^70 + x^5 + x^3 + x + 1,
  x^71 + x^6 + 1,
  x^72 + x^10 + x^9 + x^3 + 1,
  x^73 + x^25 + 1,
  x^74 + x^35 + 1,
  x^75 + x^6 + x^3 + x + 1,
  x^76 + x^21 + 1,
  x^77 + x^6 + x^5 + x^2 + 1,
  x^78 + x^6 + x^5 + x^3 + 1,
  x^79 + x^9 + 1,
  x^80 + x^9 + x^4 + x^2 + 1,
  x^81 + x^4 + 1,
  x^82 + x^8 + x^3 + x + 1,
  x^83 + x^7 + x^4 + x^2 + 1,
  x^84 + x^5 + 1,
  x^85 + x^8 + x^2 + x + 1,
  x^86 + x^21 + 1,
  x^87 + x^13 + 1,
  x^88 + x^7 + x^6 + x^2 + 1,
  x^89 + x^38 + 1,
  x^90 + x^27 + 1,
  x^91 + x^8 + x^5 + x + 1,
  x^92 + x^21 + 1,
  x^93 + x^2 + 1,
  x^94 + x^21 + 1,
  x^95 + x^11 + 1,
  x^96 + x^10 + x^9 + x^6 + 1,
  x^97 + x^6 + 1,
  x^98 + x^11 + 1,
  x^99 + x^6 + x^3 + x + 1,
  x^100 + x^15 + 1,
  x^101 + x^7 + x^6 + x + 1,
  x^102 + x^29 + 1,
  x^103 + x^9 + 1,
  x^104 + x^4 + x^3 + x + 1,
  x^105 + x^4 + 1,
  x^106 + x^15 + 1,
  x^107 + x^9 + x^7 + x^4 + 1,
  x^108 + x^17 + 1,
  x^109 + x^5 + x^4 + x^2 + 1,
  x^110 + x^33 + 1,
  x^111 + x^10 + 1,
  x^112 + x^5 + x^4 + x^3 + 1,
  x^113 + x^9 + 1,
  x^114 + x^5 + x^3 + x^2 + 1,
  x^115 + x^8 + x^7 + x^5 + 1,
  x^116 + x^4 + x^2 + x + 1,
  x^117 + x^5 + x^2 + x + 1,
  x^118 + x^33 + 1,
  x^119 + x^8 + 1,
  x^120 + x^4 + x^3 + x + 1,
  x^121 + x^18 + 1,
  x^122 + x^6 + x^2 + x + 1,
  x^123 + x^2 + 1,
  x^124 + x^19 + 1,
  x^125 + x^7 + x^6 + x^5 + 1,
  x^126 + x^21 + 1,
  x^127 + x + 1,
  x^128 + x^7 + x^2 + x + 1,
  x^129 + x^5 + 1,
  x^130 + x^3 + 1,
  x^131 + x^8 + x^3 + x^2 + 1,
  x^132 + x^17 + 1,
  x^133 + x^9 + x^8 + x^2 + 1,
  x^134 + x^57 + 1,
  x^135 + x^11 + 1,
  x^136 + x^5 + x^3 + x^2 + 1,
  x^137 + x^21 + 1,
  x^138 + x^8 + x^7 + x + 1,
  x^139 + x^8 + x^5 + x^3 + 1,
  x^140 + x^15 + 1,
  x^141 + x^10 + x^4 + x + 1,
  x^142 + x^21 + 1,
  x^143 + x^5 + x^3 + x^2 + 1,
  x^144 + x^7 + x^4 + x^2 + 1,
  x^145 + x^52 + 1,
  x^146 + x^71 + 1,
  x^147 + x^14 + 1,
  x^148 + x^27 + 1,
  x^149 + x^10 + x^9 + x^7 + 1,
  x^150 + x^53 + 1,
  x^151 + x^3 + 1,
  x^152 + x^6 + x^3 + x^2 + 1,
  x^153 + x + 1,
  x^154 + x^15 + 1,
  x^155 + x^62 + 1,
  x^156 + x^9 + 1,
  x^157 + x^6 + x^5 + x^2 + 1,
  x^158 + x^8 + x^6 + x^5 + 1,
  x^159 + x^31 + 1,
  x^160 + x^5 + x^3 + x^2 + 1,
  x^161 + x^18 + 1,
  x^162 + x^27 + 1,
  x^163 + x^7 + x^6 + x^3 + 1,
  x^164 + x^10 + x^8 + x^7 + 1,
  x^165 + x^9 + x^8 + x^3 + 1,
  x^166 + x^37 + 1,
  x^167 + x^6 + 1,
  x^168 + x^15 + x^3 + x^2 + 1,
  x^169 + x^34 + 1,
  x^170 + x^11 + 1,
  x^171 + x^6 + x^5 + x^2 + 1,
  x^172 + x + 1,
  x^173 + x^8 + x^5 + x^2 + 1,
  x^174 + x^13 + 1,
  x^175 + x^6 + 1,
  x^176 + x^11 + x^3 + x^2 + 1,
  x^177 + x^8 + 1,
  x^178 + x^31 + 1,
  x^179 + x^4 + x^2 + x + 1,
  x^180 + x^3 + 1,
  x^181 + x^7 + x^6 + x + 1,
  x^182 + x^81 + 1,
  x^183 + x^56 + 1,
  x^184 + x^9 + x^8 + x^7 + 1,
  x^185 + x^24 + 1,
  x^186 + x^11 + 1,
  x^187 + x^7 + x^6 + x^5 + 1,
  x^188 + x^6 + x^5 + x^2 + 1,
  x^189 + x^6 + x^5 + x^2 + 1,
  x^190 + x^8 + x^7 + x^6 + 1,
  x^191 + x^9 + 1,
  x^192 + x^7 + x^2 + x + 1,
  x^193 + x^15 + 1,
  x^194 + x^87 + 1,
  x^195 + x^8 + x^3 + x^2 + 1,
  x^196 + x^3 + 1,
  x^197 + x^9 + x^4 + x^2 + 1,
  x^198 + x^9 + 1,
  x^199 + x^34 + 1,
  x^200 + x^5 + x^3 + x^2 + 1,
  x^201 + x^14 + 1,
  x^202 + x^55 + 1,
  x^203 + x^8 + x^7 + x + 1,
  x^204 + x^27 + 1,
  x^205 + x^9 + x^5 + x^2 + 1,
  x^206 + x^10 + x^9 + x^5 + 1,
  x^207 + x^43 + 1,
  x^208 + x^9 + x^3 + x + 1,
  x^209 + x^6 + 1,
  x^210 + x^7 + 1,
  x^211 + x^11 + x^10 + x^8 + 1,
  x^212 + x^105 + 1,
  x^213 + x^6 + x^5 + x^2 + 1,
  x^214 + x^73 + 1,
  x^215 + x^23 + 1,
  x^216 + x^7 + x^3 + x + 1,
  x^217 + x^45 + 1,
  x^218 + x^11 + 1,
  x^219 + x^8 + x^4 + x + 1,
  x^220 + x^7 + 1,
  x^221 + x^8 + x^6 + x^2 + 1,
  x^222 + x^5 + x^4 + x^2 + 1,
  x^223 + x^33 + 1,
  x^224 + x^9 + x^8 + x^3 + 1,
  x^225 + x^32 + 1,
  x^226 + x^10 + x^7 + x^3 + 1,
  x^227 + x^10 + x^9 + x^4 + 1,
  x^228 + x^113 + 1,
  x^229 + x^10 + x^4 + x + 1,
  x^230 + x^8 + x^7 + x^6 + 1,
  x^231 + x^26 + 1,
  x^232 + x^9 + x^4 + x^2 + 1,
  x^233 + x^74 + 1,
  x^234 + x^31 + 1,
  x^235 + x^9 + x^6 + x + 1,
  x^236 + x^5 + 1,
  x^237 + x^7 + x^4 + x + 1,
  x^238 + x^73 + 1,
  x^239 + x^36 + 1,
  x^240 + x^8 + x^5 + x^3 + 1,
  x^241 + x^70 + 1,
  x^242 + x^95 + 1,
  x^243 + x^8 + x^5 + x + 1,
  x^244 + x^111 + 1,
  x^245 + x^6 + x^4 + x + 1,
  x^246 + x^11 + x^2 + x + 1,
  x^247 + x^82 + 1,
  x^248 + x^15 + x^14 + x^10 + 1,
  x^249 + x^35 + 1,
  x^250 + x^103 + 1,
  x^251 + x^7 + x^4 + x^2 + 1,
  x^252 + x^15 + 1,
  x^253 + x^46 + 1,
  x^254 + x^7 + x^2 + x + 1,
  x^255 + x^52 + 1,
  x^256 + x^10 + x^5 + x^2 + 1,
  x^257 + x^12 + 1,
  x^258 + x^71 + 1,
  x^259 + x^10 + x^6 + x^2 + 1,
  x^260 + x^15 + 1,
  x^261 + x^7 + x^6 + x^4 + 1,
  x^262 + x^9 + x^8 + x^4 + 1,
  x^263 + x^93 + 1,
  x^264 + x^9 + x^6 + x^2 + 1,
  x^265 + x^42 + 1,
  x^266 + x^47 + 1,
  x^267 + x^8 + x^6 + x^3 + 1,
  x^268 + x^25 + 1,
  x^269 + x^7 + x^6 + x + 1,
  x^270 + x^53 + 1,
  x^271 + x^58 + 1,
  x^272 + x^9 + x^3 + x^2 + 1,
  x^273 + x^23 + 1,
  x^274 + x^67 + 1,
  x^275 + x^11 + x^10 + x^9 + 1,
  x^276 + x^63 + 1,
  x^277 + x^12 + x^6 + x^3 + 1,
  x^278 + x^5 + 1,
  x^279 + x^5 + 1,
  x^280 + x^9 + x^5 + x^2 + 1,
  x^281 + x^93 + 1,
  x^282 + x^35 + 1,
  x^283 + x^12 + x^7 + x^5 + 1,
  x^284 + x^53 + 1,
  x^285 + x^10 + x^7 + x^5 + 1,
  x^286 + x^69 + 1,
  x^287 + x^71 + 1,
  x^288 + x^11 + x^10 + x + 1,
  x^289 + x^21 + 1,
  x^290 + x^5 + x^3 + x^2 + 1,
  x^291 + x^12 + x^11 + x^5 + 1,
  x^292 + x^37 + 1,
  x^293 + x^11 + x^6 + x + 1,
  x^294 + x^33 + 1,
  x^295 + x^48 + 1,
  x^296 + x^7 + x^3 + x^2 + 1,
  x^297 + x^5 + 1,
  x^298 + x^11 + x^8 + x^4 + 1,
  x^299 + x^11 + x^6 + x^4 + 1,
  x^300 + x^5 + 1,
  x^301 + x^9 + x^5 + x^2 + 1,
  x^302 + x^41 + 1,
  x^303 + x + 1,
  x^304 + x^11 + x^2 + x + 1,
  x^305 + x^102 + 1,
  x^306 + x^7 + x^3 + x + 1,
  x^307 + x^8 + x^4 + x^2 + 1,
  x^308 + x^15 + 1,
  x^309 + x^10 + x^6 + x^4 + 1,
  x^310 + x^93 + 1,
  x^311 + x^7 + x^5 + x^3 + 1,
  x^312 + x^9 + x^7 + x^4 + 1,
  x^313 + x^79 + 1,
  x^314 + x^15 + 1,
  x^315 + x^10 + x^9 + x + 1,
  x^316 + x^63 + 1,
  x^317 + x^7 + x^4 + x^2 + 1,
  x^318 + x^45 + 1,
  x^319 + x^36 + 1,
  x^320 + x^4 + x^3 + x + 1,
  x^321 + x^31 + 1,
  x^322 + x^67 + 1,
  x^323 + x^10 + x^3 + x + 1,
  x^324 + x^51 + 1,
  x^325 + x^10 + x^5 + x^2 + 1,
  x^326 + x^10 + x^3 + x + 1,
  x^327 + x^34 + 1,
  x^328 + x^8 + x^3 + x + 1,
  x^329 + x^50 + 1,
  x^330 + x^99 + 1,
  x^331 + x^10 + x^6 + x^2 + 1,
  x^332 + x^89 + 1,
  x^333 + x^2 + 1,
  x^334 + x^5 + x^2 + x + 1,
  x^335 + x^10 + x^7 + x^2 + 1,
  x^336 + x^7 + x^4 + x + 1,
  x^337 + x^55 + 1,
  x^338 + x^4 + x^3 + x + 1,
  x^339 + x^16 + x^10 + x^7 + 1,
  x^340 + x^45 + 1,
  x^341 + x^10 + x^8 + x^6 + 1,
  x^342 + x^125 + 1,
  x^343 + x^75 + 1,
  x^344 + x^7 + x^2 + x + 1,
  x^345 + x^22 + 1,
  x^346 + x^63 + 1,
  x^347 + x^11 + x^10 + x^3 + 1,
  x^348 + x^103 + 1,
  x^349 + x^6 + x^5 + x^2 + 1,
  x^350 + x^53 + 1,
  x^351 + x^34 + 1,
  x^352 + x^13 + x^11 + x^6 + 1,
  x^353 + x^69 + 1,
  x^354 + x^99 + 1,
  x^355 + x^6 + x^5 + x + 1,
  x^356 + x^10 + x^9 + x^7 + 1,
  x^357 + x^11 + x^10 + x^2 + 1,
  x^358 + x^57 + 1,
  x^359 + x^68 + 1,
  x^360 + x^5 + x^3 + x^2 + 1,
  x^361 + x^7 + x^4 + x + 1,
  x^362 + x^63 + 1,
  x^363 + x^8 + x^5 + x^3 + 1,
  x^364 + x^9 + 1,
  x^365 + x^9 + x^6 + x^5 + 1,
  x^366 + x^29 + 1,
  x^367 + x^21 + 1,
  x^368 + x^7 + x^3 + x^2 + 1,
  x^369 + x^91 + 1,
  x^370 + x^139 + 1,
  x^371 + x^8 + x^3 + x^2 + 1,
  x^372 + x^111 + 1,
  x^373 + x^8 + x^7 + x^2 + 1,
  x^374 + x^8 + x^6 + x^5 + 1,
  x^375 + x^16 + 1,
  x^376 + x^8 + x^7 + x^5 + 1,
  x^377 + x^41 + 1,
  x^378 + x^43 + 1,
  x^379 + x^10 + x^8 + x^5 + 1,
  x^380 + x^47 + 1,
  x^381 + x^5 + x^2 + x + 1,
  x^382 + x^81 + 1,
  x^383 + x^90 + 1,
  x^384 + x^12 + x^3 + x^2 + 1,
  x^385 + x^6 + 1,
  x^386 + x^83 + 1,
  x^387 + x^8 + x^7 + x + 1,
  x^388 + x^159 + 1,
  x^389 + x^10 + x^9 + x^5 + 1,
  x^390 + x^9 + 1,
  x^391 + x^28 + 1,
  x^392 + x^13 + x^10 + x^6 + 1,
  x^393 + x^7 + 1,
  x^394 + x^135 + 1,
  x^395 + x^11 + x^6 + x^5 + 1,
  x^396 + x^25 + 1,
  x^397 + x^12 + x^7 + x^6 + 1,
  x^398 + x^7 + x^6 + x^2 + 1,
  x^399 + x^26 + 1,
  x^400 + x^5 + x^3 + x^2 + 1,
  x^401 + x^152 + 1,
  x^402 + x^171 + 1,
  x^403 + x^9 + x^8 + x^5 + 1,
  x^404 + x^65 + 1,
  x^405 + x^13 + x^8 + x^2 + 1,
  x^406 + x^141 + 1,
  x^407 + x^71 + 1,
  x^408 + x^5 + x^3 + x^2 + 1,
  x^409 + x^87 + 1,
  x^410 + x^10 + x^4 + x^3 + 1,
  x^411 + x^12 + x^10 + x^3 + 1,
  x^412 + x^147 + 1,
  x^413 + x^10 + x^7 + x^6 + 1,
  x^414 + x^13 + 1,
  x^415 + x^102 + 1,
  x^416 + x^9 + x^5 + x^2 + 1,
  x^417 + x^107 + 1,
  x^418 + x^199 + 1,
  x^419 + x^15 + x^5 + x^4 + 1,
  x^420 + x^7 + 1,
  x^421 + x^5 + x^4 + x^2 + 1,
  x^422 + x^149 + 1,
  x^423 + x^25 + 1,
  x^424 + x^9 + x^7 + x^2 + 1,
  x^425 + x^12 + 1,
  x^426 + x^63 + 1,
  x^427 + x^11 + x^6 + x^5 + 1,
  x^428 + x^105 + 1,
  x^429 + x^10 + x^8 + x^7 + 1,
  x^430 + x^14 + x^6 + x + 1,
  x^431 + x^120 + 1,
  x^432 + x^13 + x^4 + x^3 + 1,
  x^433 + x^33 + 1,
  x^434 + x^12 + x^11 + x^5 + 1,
  x^435 + x^12 + x^9 + x^5 + 1,
  x^436 + x^165 + 1,
  x^437 + x^6 + x^2 + x + 1,
  x^438 + x^65 + 1,
  x^439 + x^49 + 1,
  x^440 + x^4 + x^3 + x + 1,
  x^441 + x^7 + 1,
  x^442 + x^7 + x^5 + x^2 + 1,
  x^443 + x^10 + x^6 + x + 1,
  x^444 + x^81 + 1,
  x^445 + x^7 + x^6 + x^4 + 1,
  x^446 + x^105 + 1,
  x^447 + x^73 + 1,
  x^448 + x^11 + x^6 + x^4 + 1,
  x^449 + x^134 + 1,
  x^450 + x^47 + 1,
  x^451 + x^16 + x^10 + x + 1,
  x^452 + x^6 + x^5 + x^4 + 1,
  x^453 + x^15 + x^6 + x^4 + 1,
  x^454 + x^8 + x^6 + x + 1,
  x^455 + x^38 + 1,
  x^456 + x^18 + x^9 + x^6 + 1,
  x^457 + x^16 + 1,
  x^458 + x^203 + 1,
  x^459 + x^12 + x^5 + x^2 + 1,
  x^460 + x^19 + 1,
  x^461 + x^7 + x^6 + x + 1,
  x^462 + x^73 + 1,
  x^463 + x^93 + 1,
  x^464 + x^19 + x^18 + x^13 + 1,
  x^465 + x^31 + 1,
  x^466 + x^14 + x^11 + x^6 + 1,
  x^467 + x^11 + x^6 + x + 1,
  x^468 + x^27 + 1,
  x^469 + x^9 + x^5 + x^2 + 1,
  x^470 + x^9 + 1,
  x^471 + x + 1,
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  x^3706 + x^1195 + 1,
  x^3707 + x^11 + x^6 + x + 1,
  x^3708 + x^147 + 1,
  x^3709 + x^16 + x^14 + x^6 + 1,
  x^3710 + x^797 + 1,
  x^3711 + x^1735 + 1,
  x^3712 + x^13 + x^12 + x^7 + 1,
  x^3713 + x^413 + 1,
  x^3714 + x^459 + 1,
  x^3715 + x^20 + x^18 + x^11 + 1,
  x^3716 + x^24 + x^11 + x^4 + 1,
  x^3717 + x^18 + x^15 + x^4 + 1,
  x^3718 + x^23 + x^18 + x^10 + 1,
  x^3719 + x^488 + 1,
  x^3720 + x^17 + x^15 + x^11 + 1,
  x^3721 + x^31 + 1,
  x^3722 + x^15 + x^7 + x^5 + 1,
  x^3723 + x^18 + x^6 + x^4 + 1,
  x^3724 + x^10 + x^9 + x^8 + 1,
  x^3725 + x^21 + x^14 + x^8 + 1,
  x^3726 + x^609 + 1,
  x^3727 + x^42 + 1,
  x^3728 + x^9 + x^4 + x^2 + 1,
  x^3729 + x^184 + 1,
  x^3730 + x^1191 + 1,
  x^3731 + x^26 + x^20 + x^5 + 1,
  x^3732 + x^1327 + 1,
  x^3733 + x^8 + x^7 + x^3 + 1,
  x^3734 + x^1305 + 1,
  x^3735 + x^46 + 1,
  x^3736 + x^33 + x^22 + x^18 + 1,
  x^3737 + x^287 + 1,
  x^3738 + x^75 + 1,
  x^3739 + x^18 + x^10 + x^5 + 1,
  x^3740 + x^95 + 1,
  x^3741 + x^16 + x^15 + x^4 + 1,
  x^3742 + x^25 + x^18 + x^11 + 1,
  x^3743 + x^279 + 1,
  x^3744 + x^27 + x^14 + x^2 + 1,
  x^3745 + x^684 + 1,
  x^3746 + x^22 + x^9 + x^7 + 1,
  x^3747 + x^32 + x^22 + x^11 + 1,
  x^3748 + x^19 + x^11 + x^8 + 1,
  x^3749 + x^15 + x^4 + x + 1,
  x^3750 + x^1013 + 1,
  x^3751 + x^435 + 1,
  x^3752 + x^9 + x^4 + x^2 + 1,
  x^3753 + x^407 + 1,
  x^3754 + x^1611 + 1,
  x^3755 + x^15 + x^13 + x^8 + 1,
  x^3756 + x^291 + 1,
  x^3757 + x^18 + x^16 + x^5 + 1,
  x^3758 + x^21 + x^20 + x^9 + 1,
  x^3759 + x^208 + 1,
  x^3760 + x^23 + x^9 + x + 1,
  x^3761 + x^30 + 1,
  x^3762 + x^383 + 1,
  x^3763 + x^23 + x^10 + x^2 + 1,
  x^3764 + x^1307 + 1,
  x^3765 + x^28 + x^19 + x^12 + 1,
  x^3766 + x^21 + x^15 + x + 1,
  x^3767 + x^672 + 1,
  x^3768 + x^14 + x^7 + x^2 + 1,
  x^3769 + x^300 + 1,
  x^3770 + x^107 + 1,
  x^3771 + x^13 + x^10 + x^9 + 1,
  x^3772 + x^61 + 1,
  x^3773 + x^10 + x^9 + x^4 + 1,
  x^3774 + x^24 + x^9 + x^4 + 1,
  x^3775 + x^1416 + 1,
  x^3776 + x^7 + x^5 + x^4 + 1,
  x^3777 + x^1414 + 1,
  x^3778 + x^9 + x^5 + x + 1,
  x^3779 + x^23 + x^8 + x^2 + 1,
  x^3780 + x^63 + 1,
  x^3781 + x^10 + x^9 + x^6 + 1,
  x^3782 + x^1785 + 1,
  x^3783 + x^272 + 1,
  x^3784 + x^29 + x^13 + x^6 + 1,
  x^3785 + x^87 + 1,
  x^3786 + x^1027 + 1,
  x^3787 + x^14 + x^6 + x + 1,
  x^3788 + x^1173 + 1,
  x^3789 + x^16 + x^15 + x^4 + 1,
  x^3790 + x^22 + x^21 + x^17 + 1,
  x^3791 + x^45 + 1,
  x^3792 + x^20 + x^7 + x^5 + 1,
  x^3793 + x^481 + 1,
  x^3794 + x^17 + x^4 + x^3 + 1,
  x^3795 + x^8 + x^7 + x^5 + 1,
  x^3796 + x^127 + 1,
  x^3797 + x^16 + x^8 + x^6 + 1,
  x^3798 + x^1337 + 1,
  x^3799 + x^202 + 1,
  x^3800 + x^24 + x^23 + x^21 + 1,
  x^3801 + x^112 + 1,
  x^3802 + x^16 + x^15 + x^8 + 1,
  x^3803 + x^18 + x^15 + x^6 + 1,
  x^3804 + x^349 + 1,
  x^3805 + x^18 + x^12 + x^9 + 1,
  x^3806 + x^9 + x^7 + x^5 + 1,
  x^3807 + x^68 + 1,
  x^3808 + x^29 + x^18 + x^4 + 1,
  x^3809 + x^938 + 1,
  x^3810 + x^323 + 1,
  x^3811 + x^9 + x^8 + x^4 + 1,
  x^3812 + x^1799 + 1,
  x^3813 + x^11 + x^8 + x^7 + 1,
  x^3814 + x^22 + x^21 + x^11 + 1,
  x^3815 + x^143 + 1,
  x^3816 + x^19 + x^13 + x^9 + 1,
  x^3817 + x^252 + 1,
  x^3818 + x^17 + x^8 + x^6 + 1,
  x^3819 + x^16 + x^6 + x^3 + 1,
  x^3820 + x^20 + x^11 + x^3 + 1,
  x^3821 + x^8 + x^7 + x^6 + 1,
  x^3822 + x^29 + 1,
  x^3823 + x^609 + 1,
  x^3824 + x^19 + x^13 + x^2 + 1,
  x^3825 + x^437 + 1,
  x^3826 + x^23 + x^8 + x + 1,
  x^3827 + x^18 + x^13 + x^8 + 1,
  x^3828 + x^1217 + 1,
  x^3829 + x^13 + x^9 + x^6 + 1,
  x^3830 + x^713 + 1,
  x^3831 + x^310 + 1,
  x^3832 + x^35 + x^13 + x^2 + 1,
  x^3833 + x^35 + 1,
  x^3834 + x^567 + 1,
  x^3835 + x^15 + x^5 + x^4 + 1,
  x^3836 + x^681 + 1,
  x^3837 + x^22 + x^18 + x^3 + 1,
  x^3838 + x^273 + 1,
  x^3839 + x^503 + 1,
  x^3840 + x^27 + x^9 + x + 1,
  x^3841 + x^840 + 1,
  x^3842 + x^1331 + 1,
  x^3843 + x^16 + x^5 + x^2 + 1,
  x^3844 + x^1063 + 1,
  x^3845 + x^11 + x^10 + x^9 + 1,
  x^3846 + x^693 + 1,
  x^3847 + x^108 + 1,
  x^3848 + x^29 + x^18 + x^13 + 1,
  x^3849 + x^71 + 1,
  x^3850 + x^583 + 1,
  x^3851 + x^29 + x^24 + x^19 + 1,
  x^3852 + x^169 + 1,
  x^3853 + x^12 + x^7 + x^5 + 1,
  x^3854 + x^765 + 1,
  x^3855 + x^1399 + 1,
  x^3856 + x^39 + x^25 + x^3 + 1,
  x^3857 + x^50 + 1,
  x^3858 + x^459 + 1,
  x^3859 + x^14 + x^8 + x^7 + 1,
  x^3860 + x^35 + 1,
  x^3861 + x^31 + x^10 + x^2 + 1,
  x^3862 + x^18 + x^16 + x^5 + 1,
  x^3863 + x^834 + 1,
  x^3864 + x^19 + x^15 + x^9 + 1,
  x^3865 + x^289 + 1,
  x^3866 + x^315 + 1,
  x^3867 + x^20 + x^14 + x^6 + 1,
  x^3868 + x^13 + x^12 + x^9 + 1,
  x^3869 + x^24 + x^22 + x^13 + 1,
  x^3870 + x^913 + 1,
  x^3871 + x^264 + 1,
  x^3872 + x^10 + x^3 + x^2 + 1,
  x^3873 + x^32 + 1,
  x^3874 + x^20 + x^8 + x^3 + 1,
  x^3875 + x^11 + x^10 + x^4 + 1,
  x^3876 + x^157 + 1,
  x^3877 + x^17 + x^11 + x^4 + 1,
  x^3878 + x^19 + x^9 + x^2 + 1,
  x^3879 + x^121 + 1,
  x^3880 + x^27 + x^5 + x + 1,
  x^3881 + x^810 + 1,
  x^3882 + x^1775 + 1,
  x^3883 + x^20 + x^9 + x^2 + 1,
  x^3884 + x^45 + 1,
  x^3885 + x^15 + x^8 + x^3 + 1,
  x^3886 + x^273 + 1,
  x^3887 + x^915 + 1,
  x^3888 + x^45 + x^42 + x^6 + 1,
  x^3889 + x^340 + 1,
  x^3890 + x^20 + x^19 + x^10 + 1,
  x^3891 + x^17 + x^9 + x^2 + 1,
  x^3892 + x^289 + 1,
  x^3893 + x^16 + x^13 + x^2 + 1,
  x^3894 + x^1197 + 1,
  x^3895 + x^777 + 1,
  x^3896 + x^15 + x^7 + x^5 + 1,
  x^3897 + x^310 + 1,
  x^3898 + x^25 + x^9 + x + 1,
  x^3899 + x^21 + x^20 + x^12 + 1,
  x^3900 + x^65 + 1,
  x^3901 + x^26 + x^6 + x + 1,
  x^3902 + x^1845 + 1,
  x^3903 + x^350 + 1,
  x^3904 + x^17 + x^13 + x^2 + 1,
  x^3905 + x^26 + 1,
  x^3906 + x^251 + 1,
  x^3907 + x^15 + x^4 + x + 1,
  x^3908 + x^855 + 1,
  x^3909 + x^14 + x^12 + x^11 + 1,
  x^3910 + x^28 + x^22 + x^13 + 1,
  x^3911 + x^1673 + 1,
  x^3912 + x^24 + x^11 + x^2 + 1,
  x^3913 + x^393 + 1,
  x^3914 + x^531 + 1,
  x^3915 + x^25 + x^22 + x^9 + 1,
  x^3916 + x^445 + 1,
  x^3917 + x^16 + x^12 + x^11 + 1,
  x^3918 + x^117 + 1,
  x^3919 + x^285 + 1,
  x^3920 + x^15 + x^13 + x^8 + 1,
  x^3921 + x^785 + 1,
  x^3922 + x^26 + x^21 + x + 1,
  x^3923 + x^24 + x^21 + x^3 + 1,
  x^3924 + x^245 + 1,
  x^3925 + x^18 + x^16 + x^5 + 1,
  x^3926 + x^17 + x^16 + x^12 + 1,
  x^3927 + x^367 + 1,
  x^3928 + x^8 + x^7 + x^5 + 1,
  x^3929 + x^1440 + 1,
  x^3930 + x^199 + 1,
  x^3931 + x^23 + x^9 + x^4 + 1,
  x^3932 + x^1563 + 1,
  x^3933 + x^30 + x^19 + x^3 + 1,
  x^3934 + x^28 + x^12 + x^5 + 1,
  x^3935 + x^20 + x^15 + x^8 + 1,
  x^3936 + x^15 + x^5 + x^3 + 1,
  x^3937 + x^252 + 1,
  x^3938 + x^1835 + 1,
  x^3939 + x^28 + x^19 + x^10 + 1,
  x^3940 + x^21 + x^5 + x^2 + 1,
  x^3941 + x^19 + x^11 + x^6 + 1,
  x^3942 + x^57 + 1,
  x^3943 + x^1125 + 1,
  x^3944 + x^31 + x^29 + x^28 + 1,
  x^3945 + x^427 + 1,
  x^3946 + x^1155 + 1,
  x^3947 + x^22 + x^10 + x^5 + 1,
  x^3948 + x^293 + 1,
  x^3949 + x^28 + x^22 + x^3 + 1,
  x^3950 + x^873 + 1,
  x^3951 + x^752 + 1,
  x^3952 + x^11 + x^6 + x^5 + 1,
  x^3953 + x^698 + 1,
  x^3954 + x^503 + 1,
  x^3955 + x^24 + x^8 + x^5 + 1,
  x^3956 + x^429 + 1,
  x^3957 + x^18 + x^16 + x^10 + 1,
  x^3958 + x^27 + x^4 + x^2 + 1,
  x^3959 + x^891 + 1,
  x^3960 + x^29 + x^15 + x^2 + 1,
  x^3961 + x^756 + 1,
  x^3962 + x^255 + 1,
  x^3963 + x^13 + x^8 + x + 1,
  x^3964 + x^735 + 1,
  x^3965 + x^14 + x^3 + x^2 + 1,
  x^3966 + x^337 + 1,
  x^3967 + x^357 + 1,
  x^3968 + x^25 + x^18 + x^14 + 1,
  x^3969 + x^196 + 1,
  x^3970 + x^163 + 1,
  x^3971 + x^10 + x^7 + x^2 + 1,
  x^3972 + x^595 + 1,
  x^3973 + x^13 + x^11 + x^8 + 1,
  x^3974 + x^861 + 1,
  x^3975 + x^322 + 1,
  x^3976 + x^36 + x^3 + x + 1,
  x^3977 + x^221 + 1,
  x^3978 + x^19 + x^9 + x^7 + 1,
  x^3979 + x^25 + x^9 + x^2 + 1,
  x^3980 + x^16 + x^9 + x^4 + 1,
  x^3981 + x^21 + x^11 + x^8 + 1,
  x^3982 + x^21 + x^13 + x^8 + 1,
  x^3983 + x^11 + 1,
  x^3984 + x^19 + x^5 + x^2 + 1,
  x^3985 + x^1038 + 1,
  x^3986 + x^12 + x^8 + x^7 + 1,
  x^3987 + x^11 + x^4 + x^2 + 1,
  x^3988 + x^1017 + 1,
  x^3989 + x^6 + x^5 + x^2 + 1,
  x^3990 + x^469 + 1,
  x^3991 + x^168 + 1,
  x^3992 + x^27 + x^8 + x^6 + 1,
  x^3993 + x^1468 + 1,
  x^3994 + x^19 + x^12 + x^9 + 1,
  x^3995 + x^12 + x^9 + x^8 + 1,
  x^3996 + x^19 + 1,
  x^3997 + x^16 + x^13 + x^3 + 1,
  x^3998 + x^153 + 1,
  x^3999 + x^1250 + 1,
  x^4000 + x^31 + x^18 + x^17 + 1
];

print "Extract sequence MinWeightPolynomialWeights";
MinWeightPolynomialWeights:=[PolynomialWeight(f):f in MinWeightPolynomials];

print "Extract integer MaxDegree";
MaxDegree:=#MinWeightPolynomialWeights;