Changeset 7752:79a9f901e372

Timestamp:

12/15/07 15:22:53 (5 years ago)

Author:

William Stein <wstein@…>

Branch:

default

Message:

Trac 1258 -- referee changes and OPTIMIZATIONS

Location:

sage/coding

Files:

• code_constructions.py (modified) (2 diffs)
• linear_code.py (modified) (7 diffs)

sage/coding/code_constructions.py

@@ -133 +133 @@
         sage: C
         Linear code of length 24, dimension 12 over Finite Field of size 2
-        sage: C.minimum_distance()               # long time
+        sage: C.minimum_distance()              
         8
 
     AUTHOR: David Joyner (2007-05)
     """
-    C = BinaryGolayCode()
-    return C.extended_code()
+    v = [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]]
+    V = span(GF(2), v)
+    return LinearCodeFromVectorSpace(V)
+    #C = BinaryGolayCode()
+    #return C.extended_code()
 
 def TernaryGolayCode():
     """
-    TernaryGolayCode returns a ternary Golay code. This is a perfect [11,6,5] code.
-    It is also equivalenet to a cyclic code, with generator polynomial $g(x)=2+x^2+2x^3+x^4+x^5$. 
+    TernaryGolayCode returns a ternary Golay code. This is a perfect
+    [11,6,5] code.  It is also equivalenet to a cyclic code, with
+    generator polynomial $g(x)=2+x^2+2x^3+x^4+x^5$.
     
     EXAMPLES:
@@ -178 +182 @@
     AUTHOR: David Joyner (11-2005)
     """
-    C = TernaryGolayCode()
-    return C.extended_code()
+    v = [[1, 0, 0, 0, 0, 0, 2, 0, 1, 2, 1, 2], [0, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0], [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 2, 2], [0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 1], [0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 1]]
+    V = span(GF(3), v)
+    return LinearCodeFromVectorSpace(V)
+    #C = TernaryGolayCode()
+    #return C.extended_code()
 
 def RandomLinearCode(n,k,F):

sage/coding/linear_code.py

@@ -350 +350 @@
         sage: best_known_linear_code(10,5,GF(2))    # long time
         Linear code of length 10, dimension 5 over Finite Field of size 2
-        sage: gap.eval("C:=BestKnownLinearCode(10,5,GF(2))")
+        sage: gap.eval("C:=BestKnownLinearCode(10,5,GF(2))")     # long time
         'a linear [10,5,4]2..4 shortened code'
 
@@ -767 +767 @@
             sage: Cx
             Linear code of length 22, dimension 18 over Finite Field in a of size 2^2
- 
         """
         G = self.gen_mat()
@@ -774 +773 @@
         n = len(G.columns())
         k = len(G.rows())
-        Gstr = str(gap(G))
-        gap.eval( "G:="+Gstr )
+        g = gap(G)
+        gap.eval( "G:="+g.name())
         C = gap("GeneratorMatCode(G,GF("+str(q)+"))")
         Cx = C.ExtendedCode()
         Gx = Cx.GeneratorMat()
-        Gxs = Gx._matrix_(F)
+        Gxs = Gx._matrix_(F)           # this is the killer
         MS = MatrixSpace(F,k,n+1)
         return LinearCode(MS(Gxs))
@@ -1060 +1059 @@
             sage: G  = MS([[1,0,0,0,1,1,1,0],[0,1,1,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0]])
             sage: C  = LinearCode(G)
-            sage: gp = C.permutation_automorphism_group()
+            sage: gp = C.permutation_automorphism_group()    # long time
 
         Now type "C.module_composition_factors(gp)" to get the record printed.
@@ -1278 +1277 @@
             sage: C.zeta_polynomial()
             2/5*T^2 + 2/5*T + 1/5
-            sage: C = best_known_linear_code(6,3,GF(2))
-            sage: C.minimum_distance()
+            sage: C = best_known_linear_code(6,3,GF(2))  # long time
+            sage: C.minimum_distance()                   # long time (because of above)
             3
-            sage: C.zeta_polynomial()
+            sage: C.zeta_polynomial()                    # long time (because of above)
             2/5*T^2 + 2/5*T + 1/5
             sage: C = HammingCode(4,GF(2))
@@ -1331 +1330 @@
         EXAMPLES:
             sage: C = HammingCode(3,GF(2))
-            sage: C.chinen_polynomial() 
+            sage: C.chinen_polynomial()       # long time
             (2*sqrt(2)*t^3/5 + 2*sqrt(2)*t^2/5 + 2*t^2/5 + sqrt(2)*t/5 + 2*t/5 + 1/5)/(sqrt(2) + 1)
             sage: C = TernaryGolayCode()
-            sage: C.chinen_polynomial()
+            sage: C.chinen_polynomial()       # long time
             (6*sqrt(3)*t^3/7 + 6*sqrt(3)*t^2/7 + 6*t^2/7 + 2*sqrt(3)*t/7 + 6*t/7 + 2/7)/(2*sqrt(3) + 2)
 
@@ -1393 +1392 @@
 
         EXAMPLES:
-
+            sage: C = HammingCode(3,GF(2))
+            sage: C.zeta_function() 
+            (2/5*T^2 + 2/5*T + 1/5)/(2*T^2 - 3*T + 1)
         """
         P =  self.zeta_polynomial()