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The Covering Radius of Some Primitive Ternary BCH Codes

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Finite Fields and Applications (Fq 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

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Abstract

Let \(\mathcal{C}\) be the primitive ternary BCH code of length 3m – 1 with designed distance δ. It is shown that, when δ = 8, then the covering radius of \(\mathcal{C}\) is 7 whenever m ≥ 20 and m is even, and when δ = 14, then the covering radius of \(\mathcal{C}\) is 13 whenever m ≥ 46. The technique involves Galois-theoretic criteria on the splitting of polynomials over finite fields.

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Franken, R., Cohen, S.D. (2004). The Covering Radius of Some Primitive Ternary BCH Codes. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_14

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

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