Sequentially Encodable Codeword Stabilized Codes

$n$ -qubit, $m$ -uniform states are $[[n,\ 0,\ m+1]]$ nonde-generate quantum error correcting codes (QECC). The codeword stabilized (CWS) codes use [ $n, k, d\geq m+1$ ] classical codes and $m$ -uniform graph states to construct $[[n,\ k,\ m+1]]$ QECCs. We provide a set of conditions on the classical codes to obtain CWS codes, which can be encoded in a proposed measurement-based approach. We arrive at an explicit construction of a CWS code when the starting $m$ -uniform graph state is a cluster state of qubits on a one-dimensional lattice. The proposed encoding protocol admits sequential encoding of logical qubits, making it suitable for quantum memory applications.