Title :
Goppa codes and trace operator
Author_Institution :
GECT, Toulon Univ., La Garde, France
fDate :
1/1/1998 12:00:00 AM
Abstract :
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
Keywords :
Goppa codes; mathematical operators; polynomials; Goppa codes; bounds; code dimension; even weights; polynomial; trace operator; Information theory; Memoryless systems; Parity check codes;
Journal_Title :
Information Theory, IEEE Transactions on
