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Subclass of binary Goppa codes with minimal distance equal to the design distance

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2 Author(s)
Bezzateev, S.V. ; Fac. of Eng., Nagoya Univ., Japan ; Shekhunova, N.A.

A subclass of binary Goppa codes specified by a separable polynomial G(x)=xt+A and a subset L of elements of GF(2m ) (no element of L may be a root of G(x) and t|(2m-1), A is a tth power in {GF(2m)/{0}}, is studied. For such codes it is shown that their minimal distance is equal to the design distance d=2t+1

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Information Theory, IEEE Transactions on  (Volume:41 ,  Issue: 2 )