A1 Journal article – refereed

Long binary narrow-sense BCH codes are normal

List of Authors: Honkala I, Kaipainen Y, Tietavainen A

Publisher: SPRINGER VERLAG

Publication year: 1997

Journal: Applicable Algebra in Engineering, Communication and Computing

Journal name in source: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING

Journal acronym: APPL ALGEBR ENG COMM

Volume number: 8

Issue number: 1

Number of pages: 7

ISSN: 0938-1279

DOI: http://dx.doi.org/10.1007/s002000050052

Abstract

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.

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.