On a sequence of cyclic codes with minimum distance six

A sequence of q-ary cyclic codes is considered. For each finite field GF(q), q/spl ges/4, there is a code with parameters [n, k, d; q]=[q(q-1)+1, q(q-1)-6, 6; q]. We show that all these codes are n-, k-, and d-optimal, with only one exception. Also the dual codes are considered. Their true minimum distances are calculated in the range 4/spl les/q/spl les/32.