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.