Let E/sub m/ denote the binary (m, m-1, 2) even weight code and /spl ominus/ the Kronecker product operation. A linear code of length m/spl times/t containing E/sub m//spl ominus/(t,1,t) can be decoded efficiently using a Tanner graph and a trellis diagram together with the Wagner decoding algorithm. Thus, it is important to determine whether a given code contains such a subcode. We show that the (18,9,6) binary quadratic residue code does not contain E/sub 6//spl ominus/(3,1,3). The maximum minimum distance of such a code is 5.