Abstract
We treat binary extended cyclic codes of length 2m over F2. We introduce a class, denoted by {C (t)}2≤t≤m−1, of such codes, whose defining set is characterized by only one cyclotomic coset. We prove that they are duals of extended BCH codes. We study the divisibility of the C (t)’s, and show that it determines the divisibility of all duals of extended BCH codes. Next we obtain a lower bound on their minimum distance, that yields results for several affine-invariant codes. In particular, it gives a bound for all duals of extended BCH codes, which is interesting especially when the Carlitz-Uchiyama bound is negative.
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© 1993 Springer-Verlag Wien
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Levy-dit-Vehel, F. (1993). On Duals of Binary Primitive BCH Codes. In: Camion, P., Charpin, P., Harari, S. (eds) Eurocode ’92. International Centre for Mechanical Sciences, vol 339. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2786-5_5
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DOI: https://doi.org/10.1007/978-3-7091-2786-5_5
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82519-8
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