Generating Gabidulin codes

edit

I saw an algorithm in the paper

Ismael Gutierrez Garcia; Yesneri Zuleta Saldarriaga.
"An algorithm to generate binary Gabidulin codes using Sage."
IEEE Latin America Transactions, vol. 13, no. 5, pp. 1469-1477, May 2015,
doi: 10.1109/TLA.2015.7112004.

that can be used to generate Gabidulin codes.

When I run gab_yz(2, 2), this error occurs:

------------------------------------------------------------------------
AttributeError    Traceback (most recent call last)
<ipython-input-9-f7a4cca9f105> in <module>()
----> 1 gab_yz(Integer(3),Integer(2))
<ipython-input-8-54b8ef1a8277> in gab_yz(m, K)
     74             while y<len(pp):
     75                 CC=C[u](pp[y])
---> 76                 GP=CC.full_simplify()
     77                 y=y+Integer(1)
     78                 CL+=[R(CC)]

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (build/cythonized/sage/structure/element.c:4609)()
    485             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    486         """
--> 487         return self.getattr_from_category(name)
    488 
    489     cdef getattr_from_category(self, name):

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (build/cythonized/sage/structure/element.c:4718)()
    498         else:
    499             cls = P._abstract_element_class
--> 500         return getattr_from_other_class(self, cls, name)
    501 
    502     def __dir__(self):

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/cpython/getattr.pyx in sage.cpython.getattr.getattr_from_other_class (build/cythonized/sage/cpython/getattr.c:2614)()
    392         dummy_error_message.cls = type(self)
    393         dummy_error_message.name = name
--> 394         raise AttributeError(dummy_error_message)
    395     attribute = <object>attr
    396     # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX' object has no attribute 'full_simplify'

Here is the definition of gab_yz:

def gab_yz(m,K):
    n=m
    var('w,a')
    ratpoly.<a> = PolynomialRing(ZZ)
    qq=2^(n)
    GG=GF(qq,'a')
    Z=GG.list()
    nset=[y for y in Z if y!=0]
    N=Combinations(nset,n).list()
    U=[vector(z) for z in Z]
    mset = [w for w in U if w!=0]
    M=Combinations(mset,n).list()
    Q=[]
    i=0
    while i<len(M):
        V=VectorSpace(GF(2), n)
        V= V.subspace(M[i])
        base=V.basis()
        if len(base)==n:
           Q+=[M[i]]
        else:
            Q+=[base]
        i=i+1
    j=randint(0,len(M)-1)
    NL=Q[j]
    print('Linearly independent vectors NL=', NL)

    pp=[]
    for t in range(len(NL)):
        ss=0
        for g in range(n):
           ss+=NL[t][g]*(a^g)
           pp+=[ss]
    print('Linearly independent vectors in polynomial representation', pp)
    mj=K
    r=m
    d=mj-1
    q=2^(r)
    G= GF(q,'a')

    ratpoly.<x> = PolynomialRing(ZZ)
    L=list(G)
    N=Tuples(L,d+1).list()
    C=[]
    print('Linearized polynomial of linear degree less than',mj,':')
    ii=0
    while ii<len(N):
        s=0
        k=0
        while k<(d+1):
            s+=N[ii][k]*(x^2^(k))
            k=k+1
        ii=ii+1
        print(' ',s)
        C+=[s]
    print('Number of linearized polynomial', len(C))

    GAB=[]
    CC=[]
    SS=[]
    R=PolynomialRing(Zmod(2),'a')
    l=0
    u=0
    while u<len(C):
        CL=[]
        y=0
        if u==0:
            while y<len(pp):
                CC=0
                y=y+1
                CL+=[CC]
                GAB+=[CL]
        else:
            while y<len(pp):
                CC=C[u](pp[y])
                GP=CC.full_simplify()
                y=y+1
                CL+=[R(CC)]
            GAB+=[CL]
        u=u+1
    print('The Gabidulin code with parameters' ,[n,mj,n-mj+1],'is:')
    print('CODE_GAB=',GAB)
    print('Number of codeword is:',len(GA))