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Goppa codes and trace operator

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1 Author(s)
Veron, P. ; GECT, Toulon Univ., La Garde, France

We study Goppa codes, Γ(L,g), defined by the polynomial g(z)=a(z)TrFpms:Fps(b(z)). It is shown that the dimension of these codes never reaches the general, well-known, bound for Goppa codes. New bounds are proposed depending on the value of m and p. Furthermore, we prove that when p=2 these codes have only even weights

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Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 1 )