Long binary narrow-sense BCH codes are normal

Long binary narrow-sense BCH codes are normal

Let C be the binary narrow-sense BCH code of length n = (2m − l)/h, where m is the order of 2 modulo n. Using characters of finite fields and a theorem of Weil, and results of Vladut-Skorobogatov and Lang-Weil we prove that the code C is normal in the non-primitive case h > 1 if 2m ≥ 4(2th)4t + 2...

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Veröffentlicht in:Applicable algebra in engineering, communication and computing communication and computing, 1997-01, Vol.8 (1), p.49-55
Hauptverfasser: Honkala, Iiro, Kaipainen, Yrjö, Tietäväinen, Aimo
Format: Artikel
Sprache:eng
Schlagworte:
BCH codes
Fields (mathematics)
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Zusammenfassung:Let C be the binary narrow-sense BCH code of length n = (2m − l)/h, where m is the order of 2 modulo n. Using characters of finite fields and a theorem of Weil, and results of Vladut-Skorobogatov and Lang-Weil we prove that the code C is normal in the non-primitive case h > 1 if 2m ≥ 4(2th)4t + 2, and in the primitive case h = 1 if m ≥ m0 where the constant m0 depends only on t.
ISSN:0938-1279
1432-0622
DOI:10.1007/s002000050052