Bounds on the minimum distance of the duals of BCH codes

نویسندگان

  • Daniel Augot
  • Françoise Levy-dit-Vehel
چکیده

We consider primitive cyclic codes of length p − 1 over Fp. The codes of interest here are duals of BCH codes. For these codes, a lower bound on their minimum distance can be found via the adaptation of the Weil bound to cyclic codes (see [10]). However, this bound is of no significance for roughly half of these codes. We shall fill this gap by giving, in the first part of the paper, a lower bound for an infinite class of duals of BCH codes. Since this family is a filtration of the duals of BCH codes, the bound obtained for it induces a bound for all duals. In the second part we present a lower bound obtained by implementing an algorithmic method due to Massey and Schaub (the rankbounding algorithm). The numerical results are surprisingly higher than all previously known bounds.

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عنوان ژورنال:
  • IEEE Trans. Information Theory

دوره 42  شماره 

صفحات  -

تاریخ انتشار 1996