On the minimum distance of cyclic codes

The main result is a new lower bound for the minimum distance of cyclic codes that includes earlier bounds (i.e., BCH bound, HT bound, Roos bound). This bound is related to a second method for bounding the minimum distance of a cyclic code, which we call shifting. This method can be even stronger than the first one. For all binary cyclic codes of length
< 63
(with two exceptions), we show that our methods yield the true minimum distance. The two exceptions at the end of our list are a code and its even-weight subcode. We treat several examples of cyclic codes of length
\geq 63
.