Class for cyclic and two encoders for this class

Author: David Lucas

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

@@ -25,6 +25,7 @@ Linear codes and related constructions
    :maxdepth: 1
 
    sage/coding/binary_code
+   sage/coding/cyclic_code
    sage/coding/grs
    sage/coding/hamming_code
    sage/coding/linear_code

src/sage/coding/code_constructions.py

@@ -585,124 +585,22 @@ def BinaryGolayCode():
     V = span(B, F)
     return LinearCodeFromVectorSpace(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"""

src/sage/coding/codes_catalog.py

@@ -19,7 +19,7 @@
 # in the global namespace.
 
 from code_constructions import (BCHCode, BinaryGolayCode, CyclicCodeFromGeneratingPolynomial,
-                                CyclicCode, CyclicCodeFromCheckPolynomial, DuadicCodeEvenPair,
+                                CyclicCodeFromCheckPolynomial, DuadicCodeEvenPair,
                                 DuadicCodeOddPair, ExtendedBinaryGolayCode,
                                 ExtendedQuadraticResidueCode, ExtendedTernaryGolayCode,
                                 LinearCode, LinearCodeFromCheckMatrix,
@@ -33,6 +33,7 @@
 
 from guava import BinaryReedMullerCode, QuasiQuadraticResidueCode, RandomLinearCodeGuava
 from hamming_code import HammingCode
+from cyclic_code import CyclicCode
 
 import decoders_catalog as decoders
 import encoders_catalog as encoders