chunker: Require a random irreducible polynomial

This also implements the necessary polynomial arithmetics in F_2[X].

doc/test_irreducibility.gap

@@ -0,0 +1,25 @@
+# This file is a script for GAP and tests a list of polynomials in hexadecimal
+# for irreducibility over F_2
+
+# create x over F_2 = GF(2)
+x := Indeterminate(GF(2), "x");
+
+# test if polynomial is irreducible, i.e. the number of factors is one
+IrredPoly := function (poly)
+    return (Length(Factors(poly)) = 1);
+end;;
+
+# create a polynomial in x from the hexadecimal representation of the
+# coefficients
+Hex2Poly := function (s)
+    return ValuePol(CoefficientsQadic(IntHexString(s), 2), x);
+end;;
+
+# list of candidates, in hex
+candidates := [ "3DA3358B4DC173" ];
+
+# create real polynomials
+L := List(candidates, Hex2Poly);
+
+# filter and display the list of irreducible polynomials contained in L
+Display(Filtered(L, x -> (IrredPoly(x))));