Long binary narrow-sense BCH codes are normal

: Honkala I, Kaipainen Y, Tietavainen A

Publisher: SPRINGER VERLAG

: 1997

: Applicable Algebra in Engineering, Communication and Computing

: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING

: APPL ALGEBR ENG COMM

: 8

: 1

: 49

: 55

: 7

: 0938-1279

DOI: https://doi.org/10.1007/s002000050052

Let C be the binary narrow-sense BCH code of length n = (2(m) - 1)/h, where m is the order of 2 module n. Using characters of finite fields and a theorem of Well, and results of Vladut-Skorobogatov and Lang-Weil we prove that the code C is normal in the non-primitive case h > 1 if 2(m) greater than or equal to 4(2th)(4t+2), and in the primitive case h = 1 if m greater than or equal to m(0) where the constant m(0) depends only on t.

Mathematics