SHARE
TWEET

Untitled

a guest Aug 19th, 2019 63 Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
  1. # Corrado Zanella
  2. # A condition for scattered linearized polynomials involving Dickson matrices
  3. # Script referred-to in remark 3.7
  4.  
  5. Elenco:=[]; # The list of prime powers less than 223
  6. for q in [3..222] do
  7.   if IsPrimePowerInt(q) then Add(Elenco,q); fi;
  8. od;
  9.  
  10. n:=5;
  11. for q in Elenco do #main loop
  12.   qqq:=q^2-q;
  13.   Print("\nComputing q=",q,"...\n");
  14.   O:=0*Z(q);
  15.   U:=Z(q)^0;
  16.  
  17.   for esp in [1..q-1] do
  18.     b:=Z(q^n)^esp; # N_(q^n/q)(b) will assume all possible nonzero values
  19.     scat:=true; # scat will be true if x^q+bx^q^2 is a scattered polynomial
  20.     for x in GF(q^n) do #seeking for a solution of (6)
  21.       if x<>O then
  22.         w:=AdditiveInverse(U+Inverse(b*x^qqq));
  23.         addendo:=U; # the generic element of the sum in (6)
  24.         somma:=O; # the sum in (6)
  25.         for r in [0..n-1] do
  26.           somma:=somma+addendo; # that is, sum_{i=0}^r w^((q^i-1)/(q-1))
  27.           addendo:=w*(addendo^q); # that is, w^((q^(r+1)-1)/(q-1))
  28.         od;
  29.         if somma=O then scat:=false; Print("non scattered, "); break; fi; # found a solution of (6) - exit from 'x' loop
  30.       fi; # if x<>0
  31.     od; # end of 'x' loop
  32.   if scat then Print("\nFor b=",b," it is scattered???\n\n"); return; fi; # no solution for (6) found
  33.   od; # end of 'esp' loop
  34. od; # end of 'q' loop
RAW Paste Data
We use cookies for various purposes including analytics. By continuing to use Pastebin, you agree to our use of cookies as described in the Cookies Policy. OK, I Understand
 
Top