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# Untitled

a guest Aug 19th, 2019 63 Never
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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
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))