We introduce a class of bosonic quantum error-correcting codes, termed extended binomial codes, which generalize the structure of one-mode binomial codes by incorporating ideas from high-rate qubit stabilizer codes. These codes are constructed in close analogy to $\left[\right[n,k,d\left]\right]$ qubit codes, where the parameter $n$ corresponds to the total excitation budget rather than the number of physical qubits. Our construction achieves a significant reduction in average excitation per mode while preserving error-correcting capabilities, offering improved compatibility with hardware constraints in the strong-dispersive regime. We demonstrate that extended binomial codes not only reduce the mean excitation required for encoding but also simplify syndrome extraction and logical gate implementation, particularly the logical $\overline{X}$ operation. These advantages suggest that extended binomial codes offer a scalable and resource-efficient approach for bosonic quantum error correction.

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• Quantum communication
• Quantum error correction