Extended Irreducible Binary Sextic Goppa codes

09/28/2021

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by   Daitao Huang, et al.

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Let n (>3) be a prime number and F_2^n a finite field of 2^n elements. Let L = F_2^n∪{∞} be the support set and g(x) an irreducible polynomial of degree 6 over F_2^n. In this paper, we obtain an upper bound on the number of extended irreducible binary Goppa codes Γ(L, g) of degree 6 and length 2^n+1.