Merged to latest beta (7.4.beta6).

Author: jlavauzelle

src/doc/en/reference/coding/index.rst

@@ -25,6 +25,8 @@ Linear codes and related constructions
 .. toctree::
    :maxdepth: 1
 
+   sage/coding/binary_code
+   sage/coding/cyclic_code
    sage/coding/linear_code
    sage/coding/grs
    sage/coding/hamming_code

src/sage/coding/code_constructions.py

@@ -52,7 +52,7 @@
 from sage.modules.free_module import span
 from sage.schemes.projective.projective_space import ProjectiveSpace
 from sage.structure.sequence import Sequence, Sequence_generic
-from sage.arith.all import GCD, LCM, divisors, quadratic_residues
+from sage.arith.all import GCD, LCM, divisors, quadratic_residues, gcd
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.integer import Integer
@@ -153,9 +153,9 @@ def _is_a_splitting(S1, S2, n, return_automorphism=False):
         sage: i2_sqrd = (i2^2).quo_rem(x^n-1)[1]
         sage: i2_sqrd  == i2
         True
-        sage: C1 = codes.CyclicCodeFromGeneratingPolynomial(n,i1)
-        sage: C2 = codes.CyclicCodeFromGeneratingPolynomial(n,1-i2)
-        sage: C1.dual_code() == C2
+        sage: C1 = codes.CyclicCode(length = n, generator_pol = gcd(i1, x^n - 1))
+        sage: C2 = codes.CyclicCode(length = n, generator_pol = gcd(1-i2, x^n - 1))
+        sage: C1.dual_code().systematic_generator_matrix() == C2.systematic_generator_matrix()
         True
 
     This is a special case of Theorem 6.4.3 in [HP]_.
@@ -414,22 +414,22 @@ def BCHCode(n,delta,F,b=0):
         sage: f = x^(8)-1
         sage: g.divides(f)
         True
-        sage: C = codes.CyclicCode(8,g); C
-        Linear code of length 8, dimension 4 over Finite Field of size 3
+        sage: C = codes.CyclicCode(generator_pol = g, length = 8); C
+        [8, 4] Cyclic Code over Finite Field of size 3 with x^4 + 2*x^3 + 2*x + 2 as generator polynomial
         sage: C.minimum_distance()
         4
         sage: C = codes.BCHCode(8,3,GF(3),1); C
-        Linear code of length 8, dimension 4 over Finite Field of size 3
+        [8, 4] Cyclic Code over Finite Field of size 3 with x^4 + 2*x^3 + 2*x + 2 as generator polynomial
         sage: C.minimum_distance()
         4
         sage: C = codes.BCHCode(8,3,GF(3)); C
-        Linear code of length 8, dimension 5 over Finite Field of size 3
+        [8, 5] Cyclic Code over Finite Field of size 3 with x^3 + x^2 + 1 as generator polynomial
         sage: C.minimum_distance()
         3
         sage: C = codes.BCHCode(26, 5, GF(5), b=1); C
-        Linear code of length 26, dimension 10 over Finite Field of size 5
-
+        [26, 10] Cyclic Code over Finite Field of size 5 with x^16 + 4*x^15 + 4*x^14 + x^13 + 4*x^12 + 3*x^10 + 3*x^9 + x^8 + 3*x^7 + 3*x^6 + 4*x^4 + x^3 + 4*x^2 + 4*x + 1 as generator polynomial
     """
+    from sage.coding.cyclic_code import CyclicCode
     q = F.order()
     R = IntegerModRing(n)
     m = R(q).multiplicative_order()
@@ -446,7 +446,7 @@ def BCHCode(n,delta,F,b=0):
 
     if not(g.divides(x**n-1)):
         raise ValueError("BCH codes does not exist with the given input.")
-    return CyclicCodeFromGeneratingPolynomial(n,g)
+    return CyclicCode(generator_pol = g, length = n)
 
 
 def BinaryGolayCode():
@@ -489,124 +489,22 @@ def BinaryGolayCode():
     V = span(B, F)
     return LinearCode(V, d=7)
 
-
 def CyclicCodeFromGeneratingPolynomial(n,g,ignore=True):
-    r"""
-    If g is a polynomial over GF(q) which divides `x^n-1` then
-    this constructs the code "generated by g" (ie, the code associated
-    with the principle ideal `gR` in the ring
-    `R = GF(q)[x]/(x^n-1)` in the usual way).
-
-    The option "ignore" says to ignore the condition that (a) the
-    characteristic of the base field does not divide the length (the
-    usual assumption in the theory of cyclic codes), and (b) `g`
-    must divide `x^n-1`. If ignore=True, instead of returning
-    an error, a code generated by `gcd(x^n-1,g)` is created.
-
-    EXAMPLES::
-
-        sage: P.<x> = PolynomialRing(GF(3),"x")
-        sage: g = x-1
-        sage: C = codes.CyclicCodeFromGeneratingPolynomial(4,g); C
-        Linear code of length 4, dimension 3 over Finite Field of size 3
-        sage: P.<x> = PolynomialRing(GF(4,"a"),"x")
-        sage: g = x^3+1
-        sage: C = codes.CyclicCodeFromGeneratingPolynomial(9,g); C
-        Linear code of length 9, dimension 6 over Finite Field in a of size 2^2
-        sage: P.<x> = PolynomialRing(GF(2),"x")
-        sage: g = x^3+x+1
-        sage: C = codes.CyclicCodeFromGeneratingPolynomial(7,g); C
-        Linear code of length 7, dimension 4 over Finite Field of size 2
-        sage: C.generator_matrix()
-        [1 1 0 1 0 0 0]
-        [0 1 1 0 1 0 0]
-        [0 0 1 1 0 1 0]
-        [0 0 0 1 1 0 1]
-        sage: g = x+1
-        sage: C = codes.CyclicCodeFromGeneratingPolynomial(4,g); C
-        Linear code of length 4, dimension 3 over Finite Field of size 2
-        sage: C.generator_matrix()
-        [1 1 0 0]
-        [0 1 1 0]
-        [0 0 1 1]
-
-    On the other hand, CyclicCodeFromPolynomial(4,x) will produce a
-    ValueError including a traceback error message: "`x` must
-    divide `x^4 - 1`". You will also get a ValueError if you
-    type
-
-    ::
-
-        sage: P.<x> = PolynomialRing(GF(4,"a"),"x")
-        sage: g = x^2+1
-
-    followed by CyclicCodeFromGeneratingPolynomial(6,g). You will also
-    get a ValueError if you type
-
-    ::
-
-        sage: P.<x> = PolynomialRing(GF(3),"x")
-        sage: g = x^2-1
-        sage: C = codes.CyclicCodeFromGeneratingPolynomial(5,g); C
-        Linear code of length 5, dimension 4 over Finite Field of size 3
-
-    followed by C = CyclicCodeFromGeneratingPolynomial(5,g,False), with
-    a traceback message including "`x^2 + 2` must divide
-    `x^5 - 1`".
-    """
-    P = g.parent()
-    x = P.gen()
+    from sage.misc.superseded import deprecation
+    from sage.coding.cyclic_code import CyclicCode
+    deprecation(20100, "codes.CyclicCodeFromGeneratingPolynomial is now deprecated. Please use codes.CyclicCode instead.")
     F = g.base_ring()
-    p = F.characteristic()
-    if not(ignore) and p.divides(n):
-        raise ValueError('The characteristic %s must not divide %s'%(p,n))
-    if not(ignore) and not(g.divides(x**n-1)):
-        raise ValueError('%s must divide x^%s - 1'%(g,n))
-    gn = GCD([g,x**n-1])
-    d = gn.degree()
-    coeffs = Sequence(gn.list())
-    r1 = Sequence(coeffs+[0]*(n - d - 1))
-    Sn = SymmetricGroup(n)
-    s = Sn.gens()[0] # assumes 1st gen of S_n is (1,2,...,n)
-    rows = [permutation_action(s**(-i),r1) for i in range(n-d)]
-    MS = MatrixSpace(F,n-d,n)
-    return LinearCode(MS(rows))
-
-CyclicCode = CyclicCodeFromGeneratingPolynomial
+    return CyclicCode(length = n, generator_pol = g, field = F)
 
 def CyclicCodeFromCheckPolynomial(n,h,ignore=True):
-    r"""
-    If h is a polynomial over GF(q) which divides `x^n-1` then
-    this constructs the code "generated by `g = (x^n-1)/h`"
-    (ie, the code associated with the principle ideal `gR` in
-    the ring `R = GF(q)[x]/(x^n-1)` in the usual way). The
-    option "ignore" says to ignore the condition that the
-    characteristic of the base field does not divide the length (the
-    usual assumption in the theory of cyclic codes).
-
-    EXAMPLES::
-
-        sage: P.<x> = PolynomialRing(GF(3),"x")
-        sage: C = codes.CyclicCodeFromCheckPolynomial(4,x + 1); C
-        Linear code of length 4, dimension 1 over Finite Field of size 3
-        sage: C = codes.CyclicCodeFromCheckPolynomial(4,x^3 + x^2 + x + 1); C
-        Linear code of length 4, dimension 3 over Finite Field of size 3
-        sage: C.generator_matrix()
-        [2 1 0 0]
-        [0 2 1 0]
-        [0 0 2 1]
-    """
+    from sage.misc.superseded import deprecation
+    from sage.coding.cyclic_code import CyclicCode
+    deprecation(20100, "codes.CyclicCodeFromCheckPolynomial is now deprecated. Please use codes.CyclicCode instead.")
     P = h.parent()
     x = P.gen()
-    d = h.degree()
     F = h.base_ring()
-    p = F.characteristic()
-    if not(ignore) and p.divides(n):
-        raise ValueError('The characteristic %s must not divide %s'%(p,n))
-    if not(h.divides(x**n-1)):
-        raise ValueError('%s must divide x^%s - 1'%(h,n))
     g = P((x**n-1)/h)
-    return CyclicCodeFromGeneratingPolynomial(n,g)
+    return CyclicCode(length = n, generator_pol = g, field = F)
 
 def DuadicCodeEvenPair(F,S1,S2):
     r"""
@@ -630,9 +528,10 @@ def DuadicCodeEvenPair(F,S1,S2):
         sage: _is_a_splitting(S1,S2,11)
         True
         sage: codes.DuadicCodeEvenPair(GF(q),S1,S2)
-        (Linear code of length 11, dimension 5 over Finite Field of size 3,
-         Linear code of length 11, dimension 5 over Finite Field of size 3)
+        ([11, 5] Cyclic Code over Finite Field of size 3 with x^6 + x^4 + 2*x^3 + 2*x^2 + 2*x + 1 as generator polynomial,
+         [11, 5] Cyclic Code over Finite Field of size 3 with x^6 + 2*x^5 + 2*x^4 + 2*x^3 + x^2 + 1 as generator polynomial)
     """
+    from sage.coding.cyclic_code import CyclicCode
     n = len(S1) + len(S2) + 1
     if not _is_a_splitting(S1,S2,n):
         raise TypeError("%s, %s must be a splitting of %s."%(S1,S2,n))
@@ -649,8 +548,8 @@ def DuadicCodeEvenPair(F,S1,S2):
     x = P2.gen()
     gg1 = P2([_lift2smallest_field(c)[0] for c in g1.coefficients(sparse=False)])
     gg2 = P2([_lift2smallest_field(c)[0] for c in g2.coefficients(sparse=False)])
-    C1 = CyclicCodeFromGeneratingPolynomial(n,gg1)
-    C2 = CyclicCodeFromGeneratingPolynomial(n,gg2)
+    C1 = CyclicCode(length = n, generator_pol = gg1)
+    C2 = CyclicCode(length = n, generator_pol = gg2)
     return C1,C2
 
 def DuadicCodeOddPair(F,S1,S2):
@@ -674,11 +573,12 @@ def DuadicCodeOddPair(F,S1,S2):
         sage: _is_a_splitting(S1,S2,11)
         True
         sage: codes.DuadicCodeOddPair(GF(q),S1,S2)
-        (Linear code of length 11, dimension 6 over Finite Field of size 3,
-         Linear code of length 11, dimension 6 over Finite Field of size 3)
+        ([11, 6] Cyclic Code over Finite Field of size 3 with x^5 + x^4 + 2*x^3 + x^2 + 2 as generator polynomial,
+         [11, 6] Cyclic Code over Finite Field of size 3 with x^5 + 2*x^3 + x^2 + 2*x + 2 as generator polynomial)
 
     This is consistent with Theorem 6.1.3 in [HP]_.
     """
+    from sage.coding.cyclic_code import CyclicCode
     n = len(S1) + len(S2) + 1
     if not _is_a_splitting(S1,S2,n):
         raise TypeError("%s, %s must be a splitting of %s."%(S1,S2,n))
@@ -698,8 +598,10 @@ def DuadicCodeOddPair(F,S1,S2):
     coeffs2 = [_lift2smallest_field(c)[0] for c in (g2+j).coefficients(sparse=False)]
     gg1 = P2(coeffs1)
     gg2 = P2(coeffs2)
-    C1 = CyclicCodeFromGeneratingPolynomial(n,gg1)
-    C2 = CyclicCodeFromGeneratingPolynomial(n,gg2)
+    gg1 = gcd(gg1, x**n - 1)
+    gg2 = gcd(gg2, x**n - 1)
+    C1 = CyclicCode(length = n, generator_pol = gg1)
+    C2 = CyclicCode(length = n, generator_pol = gg2)
     return C1,C2
 
 
@@ -763,12 +665,12 @@ def ExtendedQuadraticResidueCode(n,F):
         sage: C1 = codes.QuadraticResidueCode(7,GF(2))
         sage: C2 = C1.extended_code()
         sage: C3 = codes.ExtendedQuadraticResidueCode(7,GF(2)); C3
-        Extended code coming from Linear code of length 7, dimension 4 over Finite Field of size 2
+        Extended code coming from [7, 4] Cyclic Code over Finite Field of size 2 with x^3 + x + 1 as generator polynomial
         sage: C2 == C3
         True
         sage: C = codes.ExtendedQuadraticResidueCode(17,GF(2))
         sage: C
-        Extended code coming from Linear code of length 17, dimension 9 over Finite Field of size 2
+        Extended code coming from [17, 9] Cyclic Code over Finite Field of size 2 with x^8 + x^7 + x^6 + x^4 + x^2 + x + 1 as generator polynomial
         sage: C3 = codes.QuadraticResidueCodeOddPair(7,GF(2))[0]
         sage: C3x = C3.extended_code()
         sage: C4 = codes.ExtendedQuadraticResidueCode(7,GF(2))
@@ -864,10 +766,10 @@ def QuadraticResidueCode(n,F):
 
         sage: C = codes.QuadraticResidueCode(7,GF(2))
         sage: C
-        Linear code of length 7, dimension 4 over Finite Field of size 2
+        [7, 4] Cyclic Code over Finite Field of size 2 with x^3 + x + 1 as generator polynomial
         sage: C = codes.QuadraticResidueCode(17,GF(2))
         sage: C
-        Linear code of length 17, dimension 9 over Finite Field of size 2
+        [17, 9] Cyclic Code over Finite Field of size 2 with x^8 + x^7 + x^6 + x^4 + x^2 + x + 1 as generator polynomial
         sage: C1 = codes.QuadraticResidueCodeOddPair(7,GF(2))[0]
         sage: C2 = codes.QuadraticResidueCode(7,GF(2))
         sage: C1 == C2
@@ -898,22 +800,22 @@ def QuadraticResidueCodeEvenPair(n,F):
     EXAMPLES::
 
         sage: codes.QuadraticResidueCodeEvenPair(17,GF(13))
-        (Linear code of length 17, dimension 8 over Finite Field of size 13,
-         Linear code of length 17, dimension 8 over Finite Field of size 13)
+        ([17, 8] Cyclic Code over Finite Field of size 13 with x^9 + 7*x^8 + 2*x^7 + x^6 + 6*x^5 + 7*x^4 + 12*x^3 + 11*x^2 + 6*x + 12 as generator polynomial,
+         [17, 8] Cyclic Code over Finite Field of size 13 with x^9 + 5*x^8 + 2*x^7 + x^6 + 4*x^5 + 9*x^4 + 12*x^3 + 11*x^2 + 8*x + 12 as generator polynomial)
         sage: codes.QuadraticResidueCodeEvenPair(17,GF(2))
-        (Linear code of length 17, dimension 8 over Finite Field of size 2,
-         Linear code of length 17, dimension 8 over Finite Field of size 2)
+        ([17, 8] Cyclic Code over Finite Field of size 2 with x^9 + x^6 + x^5 + x^4 + x^3 + 1 as generator polynomial,
+         [17, 8] Cyclic Code over Finite Field of size 2 with x^9 + x^8 + x^6 + x^3 + x + 1 as generator polynomial)
         sage: codes.QuadraticResidueCodeEvenPair(13,GF(9,"z"))
-        (Linear code of length 13, dimension 6 over Finite Field in z of size 3^2,
-         Linear code of length 13, dimension 6 over Finite Field in z of size 3^2)
+        ([13, 6] Cyclic Code over Finite Field in z of size 3^2 with x^7 + 2*x^6 + 2*x^5 + x^2 + x + 2 as generator polynomial,
+         [13, 6] Cyclic Code over Finite Field in z of size 3^2 with x^7 + x^5 + x^4 + 2*x^3 + 2*x^2 + 2 as generator polynomial)
         sage: C1,C2 = codes.QuadraticResidueCodeEvenPair(7,GF(2))
         sage: C1.is_self_orthogonal()
         True
         sage: C2.is_self_orthogonal()
         True
         sage: C3 = codes.QuadraticResidueCodeOddPair(17,GF(2))[0]
         sage: C4 = codes.QuadraticResidueCodeEvenPair(17,GF(2))[1]
-        sage: C3 == C4.dual_code()
+        sage: C3.systematic_generator_matrix() == C4.dual_code().systematic_generator_matrix()
         True
 
     This is consistent with Theorem 6.6.9 and Exercise 365 in [HP]_.
@@ -962,14 +864,14 @@ def QuadraticResidueCodeOddPair(n,F):
     EXAMPLES::
 
         sage: codes.QuadraticResidueCodeOddPair(17,GF(13))
-        (Linear code of length 17, dimension 9 over Finite Field of size 13,
-         Linear code of length 17, dimension 9 over Finite Field of size 13)
+        ([17, 9] Cyclic Code over Finite Field of size 13 with x^8 + 8*x^7 + 10*x^6 + 11*x^5 + 4*x^4 + 11*x^3 + 10*x^2 + 8*x + 1 as generator polynomial,
+         [17, 9] Cyclic Code over Finite Field of size 13 with x^8 + 6*x^7 + 8*x^6 + 9*x^5 + 9*x^3 + 8*x^2 + 6*x + 1 as generator polynomial)
         sage: codes.QuadraticResidueCodeOddPair(17,GF(2))
-        (Linear code of length 17, dimension 9 over Finite Field of size 2,
-         Linear code of length 17, dimension 9 over Finite Field of size 2)
+        ([17, 9] Cyclic Code over Finite Field of size 2 with x^8 + x^7 + x^6 + x^4 + x^2 + x + 1 as generator polynomial,
+         [17, 9] Cyclic Code over Finite Field of size 2 with x^8 + x^5 + x^4 + x^3 + 1 as generator polynomial)
         sage: codes.QuadraticResidueCodeOddPair(13,GF(9,"z"))
-        (Linear code of length 13, dimension 7 over Finite Field in z of size 3^2,
-         Linear code of length 13, dimension 7 over Finite Field in z of size 3^2)
+        ([13, 7] Cyclic Code over Finite Field in z of size 3^2 with x^6 + 2*x^4 + 2*x^3 + 2*x^2 + 1 as generator polynomial,
+         [13, 7] Cyclic Code over Finite Field in z of size 3^2 with x^6 + x^5 + 2*x^4 + 2*x^2 + x + 1 as generator polynomial)
         sage: C1 = codes.QuadraticResidueCodeOddPair(17,GF(2))[1]
         sage: C1x = C1.extended_code()
         sage: C2 = codes.QuadraticResidueCodeOddPair(17,GF(2))[0]

src/sage/coding/codes_catalog.py

@@ -23,7 +23,7 @@
 
 from .linear_code import LinearCode
 from .code_constructions import (BCHCode, BinaryGolayCode, CyclicCodeFromGeneratingPolynomial,
-                                CyclicCode, CyclicCodeFromCheckPolynomial, DuadicCodeEvenPair,
+                                CyclicCodeFromCheckPolynomial, DuadicCodeEvenPair,
                                 DuadicCodeOddPair, ExtendedBinaryGolayCode,
                                 ExtendedQuadraticResidueCode, ExtendedTernaryGolayCode,
                                 from_parity_check_matrix,
@@ -42,6 +42,7 @@
 
 from .guava import QuasiQuadraticResidueCode, RandomLinearCodeGuava
 _lazy_import('sage.coding.punctured_code', 'PuncturedCode')
+from .cyclic_code import CyclicCode
 from .hamming_code import HammingCode
 from . import decoders_catalog as decoders
 from . import encoders_catalog as encoders