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C x4 3x2 3 is irreducible according to Eisenstein's criterion with p = 3 d Consider x5 5x2 1 mod 2, which is x5 x2 1 It is easy to see that this polynomial has no roots in Z 2, and so to prove irreducibility in Z 2 it again suffices to show it has no quadratic factors The only quadratic polynomial in Z 2x that does not have a root in Z 2 is x 2x1 which does not divide x5 x 1About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us Creators} 6 b ¹#Ø ª%41 1 #Õ I O \0Ã Reedsolomon Codes Rongjaye Chen Reedsolomon Codes 1 Codes Rm cxc assessor

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