Long binary narrow-sense BCH codes are normal
Iiro S. Honkala, Y. Kaipainen, Aimo Tietäväinen · 2002
Let C be the binary narrow-sense BCH code of length n=(2/sup m/-1)/N and designed distance 2t+1, where m is the order of 2 module n. Using characters of finite fields and a theorem of Weil, and results of Vladut-Skorobogatov (1989) and Lang-Weil (1954) we prove that the code C is normal in the non-primitive case N>1 if 2/sup m//spl ges/4(2tN)/sup 4t+2/, and in the primitive case N=1 if m/spl ges/m/sub 0/, where the constant m/sub 0/ depends only on t.>