The McEliece cryptosystem was proposed by R.McEliece
in 1978. In its original version it is based on Goppa
codes. Given a public key matrix G and a codeword
c=mG+e, we reduce the problem of recovering the error
vector e to the shortest lattice vector problem.
Using Conway and Sloane''s "Construction A", we
construct a basis of a lattice, in which the norm of
the shortest vector w.r.t. lp norm is equal to the lp
norm of the error vector e for p>log(t), where t is
the weight of the error vector e. To find such
shortest vector in our lattice we use the LLL and
block basis reduction algorithms for the lp norm,
which guarantee only an approximation of the length
of the shortest lattice vector. Our tests show that
this attack method provides no positive results for
Goppa codes of length more than 127.