  We analyse a generalised quantum error correction code against photon loss
where a logical qubit is encoded into a subspace of a single oscillator mode
that is spanned by distinct multi-component cat states (coherent-state
superpositions). We present a systematic code construction that includes the
extension of an existing one-photon-loss code to higher numbers of losses. When
subject to a photon loss (amplitude damping) channel, the encoded qubits are
shown to exhibit a cyclic behaviour where the code and error spaces each
correspond to certain multiples of losses, half of which can be corrected. As
another generalisation we also discuss how to protect logical qudits against
photon losses, and as an application we consider a one-way quantum
communication scheme, in which the encoded qubits are periodically recovered
while the coherent-state amplitudes are restored as well at regular intervals.
