@@ -73,6 +73,9 @@ def __mul__(self, x):
7373 raise ValueError , "Two sets of elements cannot be multiplied"
7474
7575 def power_to_tuple (self ):
76+ """
77+ Convert Galois field elements from power form to tuple form representation.
78+ """
7679 y = zeros (len (self .elements ))
7780 for idx , i in enumerate (self .elements ):
7881 if 2 ** i < 2 ** self .m :
@@ -82,6 +85,9 @@ def power_to_tuple(self):
8285 return GF (y , self .m )
8386
8487 def tuple_to_power (self ):
88+ """
89+ Convert Galois field elements from tuple form to power form representation.
90+ """
8591 y = zeros (len (self .elements ))
8692 for idx , i in enumerate (self .elements ):
8793 if i != 0 :
@@ -98,13 +104,19 @@ def tuple_to_power(self):
98104 return GF (y , self .m )
99105
100106 def order (self ):
107+ """
108+ Compute the orders of the Galois field elements.
109+ """
101110 orders = zeros (len (self .elements ))
102111 power_gf = self .tuple_to_power ()
103112 for idx , i in enumerate (power_gf .elements ):
104113 orders [idx ] = (2 ** self .m - 1 )/ (gcd (i , 2 ** self .m - 1 ))
105114 return orders
106115
107116 def cosets (self ):
117+ """
118+ Compute the cyclotomic cosets of the Galois field.
119+ """
108120 coset_list = []
109121 x = self .tuple_to_power ().elements
110122 mark_list = zeros (len (x ))
@@ -127,6 +139,9 @@ def cosets(self):
127139 return coset_list
128140
129141 def minpolys (self ):
142+ """
143+ Compute the minimal polynomials for all elements of the Galois field.
144+ """
130145 minpol_list = array ([])
131146 full_gf = GF (arange (2 ** self .m ), self .m )
132147 full_cosets = full_gf .cosets ()
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