A1 Refereed original research article in a scientific journal
Long binary narrow-sense BCH codes are normal
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: 8
Issue: 1
First page : 49
Last page: 55
Number of pages: 7
ISSN: 0938-1279
DOI: https://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.
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