A new algorithm is presented for finding codewords that are of low weight ("light") and low degree ("short") in narrow-sense binary BCH codes of length n=2/sup m/-1 and minimum weight d=2/sup t/-1, for use in serial implementations. This improves on some earlier results by Roth and Scroussi (see ibid., vol.34, p.593-6, May 1998), and extends the range of parameters to include cases of interest for long CRC (cyclic redundancy codes) error-detection schemes.

A characterization of the equivalence classes of prime-length cyclic codes over any finite field is given, generalizing the binary case solved by Leon, Masely, and Pless. In the special case of cyclic(p, k)codes over GF(q), withP|(q - 1), a one-to-one correspondence between the equivelance classes and the orbits ofk-sets under the affine group, GA(1, p)is established.