Some new bounds for q-ary [n,k,d] codes

Let C[n,k,d] be a q-ary linear code and H=(H/sub 1/,H/sub 2/,...,H/sub n/) be the parity check matrix. We have proved that an [n,k,d] code with d>4 over GF(2) must satisfy k/spl les/n-d+1-log/sub 2/(n-d+1). In this paper, we generalize this bound to GF(q) by several different methods and derived some new bounds for q-ary linear block codes.