    /**************************************************************************\

    MODULE: vec_GF2E

    SUMMARY:

    Provides vectors over GF2E, along with some related operations.

    \**************************************************************************/

    #include <NTL/GF2E.h>
    #include <NTL/vector.h>

    typedef Vec<GF2E> vec_GF2E; // backward compatibility

    void mul(vec_GF2E& x, const vec_GF2E& a, const GF2E& b);
    void mul(vec_GF2E& x, const vec_GF2E& a, GF2 b);
    void mul(vec_GF2E& x, const vec_GF2E& a, long b);

    void mul(vec_GF2E& x, const GF2E& a, const vec_GF2E& b);
    void mul(vec_GF2E& x, GF2 a, const vec_GF2E& b);
    void mul(vec_GF2E& x, long a, const vec_GF2E& b);
    // x = a * b

    void add(vec_GF2E& x, const vec_GF2E& a, const vec_GF2E& b);
    // x = a + b

    void sub(vec_GF2E& x, const vec_GF2E& a, const vec_GF2E& b);
    // x = a - b = x + a

    void negate(vec_GF2E& x, const vec_GF2E& a);
    // x = - a = a

    void clear(vec_GF2E& x);
    // x = 0 (length unchanged)

    long IsZero(const vec_GF2E& a);
    // test if a is the zero vector

    void InnerProduct(GF2E& x, const vec_GF2E& a, const vec_GF2E& b);
    // x = sum_{i=0}^{n-1} a[i]*b[i], where n = min(a.length(), b.length())

    void InnerProduct(GF2E& x, const vec_GF2E& a, const vec_GF2E& b,
                      long offset);
    // x = sum_{i=offset}^{n-1} a[i]*b[i-offset], where n = min(a.length(),
    // b.length()+offset)

    void VectorCopy(vec_GF2E& x, const vec_GF2E& a, long n);
    vec_GF2E VectorCopy(const vec_GF2E& a, long n);
    // x = a copy of a of length exactly n.
    // The input is truncated or padded with zeroes, as necessary.

    void random(vec_GF2E& x, long n);  // x = random vector of length n
    vec_GF2E random_vec_GF2E(long n);

    // operator notation:

    vec_GF2E
    operator+(const vec_GF2E& a, const vec_GF2E& b);

    vec_GF2E
    operator-(const vec_GF2E& a, const vec_GF2E& b);

    vec_GF2E operator-(const vec_GF2E& a);

    // vector/scalar multiplication:

    vec_GF2E operator*(const vec_GF2E& a, const GF2E& b);
    vec_GF2E operator*(const vec_GF2E& a, GF2 b);
    vec_GF2E operator*(const vec_GF2E& a, long b);

    vec_GF2E operator*(const GF2E& a, const vec_GF2E& b);
    vec_GF2E operator*(GF2 a, const vec_GF2E& b);
    vec_GF2E operator*(long a, const vec_GF2E& b);

    // inner product:

    GF2E operator*(const vec_GF2E& a, const vec_GF2E& b);

    // assignment operator notation:

    vec_GF2E& operator+=(vec_GF2E& x, const vec_GF2E& a);
    vec_GF2E& operator-=(vec_GF2E& x, const vec_GF2E& a);

    vec_GF2E& operator*=(vec_GF2E& x, const GF2E& a);
    vec_GF2E& operator*=(vec_GF2E& x, GF2 a);
    vec_GF2E& operator*=(vec_GF2E& x, long a);

    // Implementation note: the BlockConstruct routine has been customized
    // for GF2E so that when a vec_GF2E is grown, space for the needed
    // elements is allocated in one contiguous chunk.  This saves on calls to
    // malloc and free, and should also yield better locality of reference.
    // One consequence of this is that swapping an element of a vec_GF2E
    // with another GF2E can not be implemented by pointer swap, and will in
    // this case be done by copy.