Weil-Serre Type Bounds for Cyclic Codes

Özbudak, Ferruh
We give a new method in order to obtain Weil-Serre type hounds on the minimum distance of arbitrary cyclic codes over F(pe) of length coprime to p, where e >= 1 is an arbitrary integer. In an earlier paper we obtained Weil-Serre type bounds for such codes only when e = 1 or e = 2 using lengthy explicit factorizations, which seems hopeless to generalize. The new method avoids such explicit factorizations and it produces an effective alternative. Using our method we obtain Weil-Serre type bounds in various cases. By examples we show that our bounds perform very well against Bose-Chaudhuri-Hocquenghem (BCH) bound and they yield the exact minimum distance in some cases.

Citation Formats
C. GÜNERİ and F. Özbudak, “Weil-Serre Type Bounds for Cyclic Codes,” IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 54, no. 12, pp. 5381–5395, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42541.