コード例 #1
0
ファイル: decoder.py プロジェクト: bgxcpku/sagelib
def coset_leader(C, v):
    """
    The vector v represents a received word, so should 
    be in the same ambient space V as C. Returns an
    element of the syndrome of v of lowest weight.

    EXAMPLES:
        sage: C = HammingCode(2,GF(3)); C                                  
        Linear code of length 4, dimension 2 over Finite Field of size 3   
        sage: V = VectorSpace(GF(3), 4)                                   
        sage: v = V([0, 2, 0, 1])
        sage: from sage.coding.decoder import coset_leader
        sage: coset_leader(C, v)
        ((0, 0, 1, 0), 1)       
        sage: coset_leader(C, v)[0]-v in C
        True

    """
    coset = [[c+v, hamming_weight(c+v)] for c in C]
    wts = [x[1] for x in coset]
    min_wt = min(wts)
    s = C[0]                # initializing
    w = hamming_weight(v)   # initializing
    for x in coset:
        if x[1]==min_wt:
            w = x[1]
            s = x[0]
            break
    return s,w
コード例 #2
0
def coset_leader(C, v):
    """
    The vector v represents a received word, so should 
    be in the same ambient space V as C. Returns an
    element of the syndrome of v of lowest weight.

    EXAMPLES:
        sage: C = HammingCode(2,GF(3)); C                                  
        Linear code of length 4, dimension 2 over Finite Field of size 3   
        sage: V = VectorSpace(GF(3), 4)                                   
        sage: v = V([0, 2, 0, 1])
        sage: from sage.coding.decoder import coset_leader
        sage: coset_leader(C, v)
        ((0, 0, 1, 0), 1)       
        sage: coset_leader(C, v)[0]-v in C
        True

    """
    coset = [[c + v, hamming_weight(c + v)] for c in C]
    wts = [x[1] for x in coset]
    min_wt = min(wts)
    s = C[0]  # initializing
    w = hamming_weight(v)  # initializing
    for x in coset:
        if x[1] == min_wt:
            w = x[1]
            s = x[0]
            break
    return s, w
コード例 #3
0
ファイル: decoder.py プロジェクト: bgxcpku/sagelib
def decode(C, v, algorithm="syndrome"):
    """
    The vector v represents a received word, so should 
    be in the same ambient space V as C. Returns an
    element in C which is closest to v in the Hamming 
    metric.

    Methods implemented include "nearest neighbor" (essentially
    a brute force search) and "syndrome".

    EXAMPLES:
        sage: C = HammingCode(2,GF(3))
        sage: V = VectorSpace(GF(3), 4)
        sage: v = V([0, 2, 0, 1])
        sage: v in C
        False
        sage: from sage.coding.decoder import decode
        sage: c = decode(C, v);c
        (0, 2, 2, 1)
        sage: c in C
        True
        sage: c = decode(C, v, algorithm="nearest neighbor");c
        (0, 2, 2, 1)
        sage: C = HammingCode(3,GF(3)); C
        Linear code of length 13, dimension 10 over Finite Field of size 3
        sage: V = VectorSpace(GF(3), 13)
        sage: v = V([2]+[0]*12)
        sage: decode(C, v)  # long time (9s on sage.math, 2011)
        (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
    """
    V = C.ambient_space()
    if not(type(v)==list):
        v = v.list()
    v = V(v)
    if algorithm=="nearest neighbor":
        diffs = [[c-v,hamming_weight(c-v)] for c in C]
        diffs.sort(lambda x,y:  x[1]-y[1])
        return diffs[0][0]+v
    if algorithm=="syndrome":
        return -V(syndrome(C, v)[0])+v
コード例 #4
0
def decode(C, v, algorithm="syndrome"):
    """
    The vector v represents a received word, so should 
    be in the same ambient space V as C. Returns an
    element in C which is closest to v in the Hamming 
    metric.

    Methods implemented include "nearest neighbor" (essentially
    a brute force search) and "syndrome".

    EXAMPLES:
        sage: C = HammingCode(2,GF(3))
        sage: V = VectorSpace(GF(3), 4)
        sage: v = V([0, 2, 0, 1])
        sage: v in C
        False
        sage: from sage.coding.decoder import decode
        sage: c = decode(C, v);c
        (0, 2, 2, 1)
        sage: c in C
        True
        sage: c = decode(C, v, algorithm="nearest neighbor");c
        (0, 2, 2, 1)
        sage: C = HammingCode(3,GF(3)); C
        Linear code of length 13, dimension 10 over Finite Field of size 3
        sage: V = VectorSpace(GF(3), 13)
        sage: v = V([2]+[0]*12)
        sage: decode(C, v)  # long time (9s on sage.math, 2011)
        (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
    """
    V = C.ambient_space()
    if not (type(v) == list):
        v = v.list()
    v = V(v)
    if algorithm == "nearest neighbor":
        diffs = [[c - v, hamming_weight(c - v)] for c in C]
        diffs.sort(lambda x, y: x[1] - y[1])
        return diffs[0][0] + v
    if algorithm == "syndrome":
        return -V(syndrome(C, v)[0]) + v
コード例 #5
0
ファイル: decoder.py プロジェクト: bgxcpku/sagelib
def syndrome(C, v):
    """
    The vector v represents a received word, so should 
    be in the same ambient space V as C. Returns the 
    elements in V (including v) which belong to the 
    syndrome of v (ie, the coset v+C, sorted by weight).

    EXAMPLES:
        sage: C = HammingCode(2,GF(3)); C
        Linear code of length 4, dimension 2 over Finite Field of size 3
        sage: V = VectorSpace(GF(3), 4)
        sage: v = V([0, 2, 0, 1])
        sage: from sage.coding.decoder import syndrome
        sage: syndrome(C, v)
         [(0, 0, 1, 0), (0, 2, 0, 1), (2, 0, 0, 2), (1, 1, 0, 0), (2, 2, 2, 0), (1, 0, 2, 1), (0, 1, 2, 2), (1, 2, 1, 2), (2, 1, 1, 1)]

    """
    V = C.ambient_space()
    if not(type(v)==list):
        v = v.list()
    v = V(v)
    coset = [[c+v,hamming_weight(c+v)] for c in C]
    coset.sort(lambda x,y: x[1]-y[1])
    return [x[0] for x in coset]
コード例 #6
0
def syndrome(C, v):
    """
    The vector v represents a received word, so should 
    be in the same ambient space V as C. Returns the 
    elements in V (including v) which belong to the 
    syndrome of v (ie, the coset v+C, sorted by weight).

    EXAMPLES:
        sage: C = HammingCode(2,GF(3)); C
        Linear code of length 4, dimension 2 over Finite Field of size 3
        sage: V = VectorSpace(GF(3), 4)
        sage: v = V([0, 2, 0, 1])
        sage: from sage.coding.decoder import syndrome
        sage: syndrome(C, v)
         [(0, 0, 1, 0), (0, 2, 0, 1), (2, 0, 0, 2), (1, 1, 0, 0), (2, 2, 2, 0), (1, 0, 2, 1), (0, 1, 2, 2), (1, 2, 1, 2), (2, 1, 1, 1)]

    """
    V = C.ambient_space()
    if not (type(v) == list):
        v = v.list()
    v = V(v)
    coset = [[c + v, hamming_weight(c + v)] for c in C]
    coset.sort(lambda x, y: x[1] - y[1])
    return [x[0] for x in coset]
コード例 #7
0
 def is_block_design(self):
     """
     Returns a pair True, pars if the incidence structure is a t-design,
     for some t, where pars is the list of parameters [t, v, k, lmbda].
     The largest possible t is returned, provided t=10.
     
     EXAMPLES::
     
         sage: BD = IncidenceStructure(range(7),[[0,1,2],[0,3,4],[0,5,6],[1,3,5],[1,4,6],[2,3,6],[2,4,5]])
         sage: BD.is_block_design()
         (True, [2, 7, 3, 1])
         sage: BD.block_design_checker(2, 7, 3, 1)
         True
         sage: BD = WittDesign(9)        # requires optional gap package 'design'
         sage: BD.is_block_design()      # requires optional gap package 'design'
         (True, [2, 9, 3, 1])
         sage: BD = WittDesign(12)       # requires optional gap package 'design'
         sage: BD.is_block_design()      # requires optional gap package 'design'
         (True, [5, 12, 6, 1])
         sage: BD = AffineGeometryDesign(3, 1, GF(2))
         sage: BD.is_block_design()
         (True, [2, 8, 2, 2])
     """
     from sage.combinat.designs.incidence_structures import coordinatewise_product
     from sage.combinat.combinat import unordered_tuples, combinations
     from sage.coding.linear_code import hamming_weight
     A = self.incidence_matrix()
     v = len(self.points())
     b = len(self.blocks())
     k = sum(A.columns()[0])
     rowsA = A.rows()
     VS = rowsA[0].parent()
     r = sum(rowsA[0])
     for i in range(b):
         if not (sum(A.columns()[i]) == k):
             return False
     for i in range(v):
         if not (sum(A.rows()[i]) == r):
             return False
     t_found_yet = False
     lambdas = []
     for t in range(2, min(v, 11)):
         #print t
         L1 = combinations(range(v), t)
         L2 = [[rowsA[i] for i in L] for L in L1]
         #print t,len(L2)
         lmbda = hamming_weight(VS(coordinatewise_product(L2[0])))
         lambdas.append(lmbda)
         pars = [t, v, k, lmbda]
         #print pars
         for ell in L2:
             a = hamming_weight(VS(coordinatewise_product(ell)))
             if not (a == lmbda) or a == 0:
                 if not (t_found_yet):
                     pars = [t - 1, v, k, lambdas[t - 3]]
                     return False, pars
                 else:
                     #print pars, lambdas
                     pars = [t - 1, v, k, lambdas[t - 3]]
                     return True, pars
             t_found_yet = True
     pars = [t - 1, v, k, lambdas[t - 3]]
     return True, pars
コード例 #8
0
    def is_block_design(self):
        """
        Returns a pair True, pars if the incidence structure is a t-design,
        for some t, where pars is the list of parameters [t, v, k, lmbda].
        The largest possible t is returned, provided t=10.
        
        EXAMPLES::
        
            sage: BD = IncidenceStructure(range(7),[[0,1,2],[0,3,4],[0,5,6],[1,3,5],[1,4,6],[2,3,6],[2,4,5]])
            sage: BD.is_block_design()
            (True, [2, 7, 3, 1])
            sage: BD.block_design_checker(2, 7, 3, 1)
            True
            sage: BD = WittDesign(9)        # requires optional gap package 'design'
            sage: BD.is_block_design()      # requires optional gap package 'design'
            (True, [2, 9, 3, 1])
            sage: BD = WittDesign(12)       # requires optional gap package 'design'
            sage: BD.is_block_design()      # requires optional gap package 'design'
            (True, [5, 12, 6, 1])
            sage: BD = AffineGeometryDesign(3, 1, GF(2))
            sage: BD.is_block_design()
            (True, [2, 8, 2, 2])
        """
        from sage.combinat.designs.incidence_structures import coordinatewise_product
        from sage.combinat.combinat import unordered_tuples, combinations
        from sage.coding.linear_code import hamming_weight

        A = self.incidence_matrix()
        v = len(self.points())
        b = len(self.blocks())
        k = sum(A.columns()[0])
        rowsA = A.rows()
        VS = rowsA[0].parent()
        r = sum(rowsA[0])
        for i in range(b):
            if not (sum(A.columns()[i]) == k):
                return False
        for i in range(v):
            if not (sum(A.rows()[i]) == r):
                return False
        t_found_yet = False
        lambdas = []
        for t in range(2, min(v, 11)):
            # print t
            L1 = combinations(range(v), t)
            L2 = [[rowsA[i] for i in L] for L in L1]
            # print t,len(L2)
            lmbda = hamming_weight(VS(coordinatewise_product(L2[0])))
            lambdas.append(lmbda)
            pars = [t, v, k, lmbda]
            # print pars
            for ell in L2:
                a = hamming_weight(VS(coordinatewise_product(ell)))
                if not (a == lmbda) or a == 0:
                    if not (t_found_yet):
                        pars = [t - 1, v, k, lambdas[t - 3]]
                        return False, pars
                    else:
                        # print pars, lambdas
                        pars = [t - 1, v, k, lambdas[t - 3]]
                        return True, pars
                t_found_yet = True
        pars = [t - 1, v, k, lambdas[t - 3]]
        return True, pars