کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4582855 1630374 2014 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
New identities relating wild Goppa codes
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
New identities relating wild Goppa codes
چکیده انگلیسی

For a given support L∈Fqmn and a polynomial g∈Fqm[x]g∈Fqm[x] with no roots in FqmFqm, we prove equality between the q  -ary Goppa codes Γq(L,N(g))=Γq(L,N(g)/g)Γq(L,N(g))=Γq(L,N(g)/g) where N(g)N(g) denotes the norm of g  , that is gqm−1+⋯+q+1gqm−1+⋯+q+1. In particular, for m=2m=2, that is, for a quadratic extension, we get Γq(L,gq)=Γq(L,gq+1)Γq(L,gq)=Γq(L,gq+1). If g   has roots in FqmFqm, then we do not necessarily have equality and we prove that the difference of the dimensions of the two codes is bounded above by the number of distinct roots of g   in FqmFqm. These identities provide numerous code equivalences and improved designed parameters for some families of classical Goppa codes.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 29, September 2014, Pages 178–197
نویسندگان
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