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A Note on Quantum Hamming Bound

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arxiv 0711.4603 v1 pith:FLNLBTPJ submitted 2007-11-29 quant-ph cs.ITmath.IT

Salah A. Aly This is my paper · ORCID
classification quant-phcs.ITmath.IT
keywords boundcodesstabilizerdegeneratedoubleerror-correctinghammingnote
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Proving the quantum Hamming bound for degenerate nonbinary stabilizer codes has been an open problem for a decade. In this note, I prove this bound for double error-correcting degenerate stabilizer codes. Also, I compute the maximum length of single and double error-correcting MDS stabilizer codes over finite fields.

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Cited by 2 Pith papers

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  1. Compressing Syndrome Measurement Sequences

    quant-ph 2025-09 conditional novelty 7.0 of 10

    Fault-tolerant syndrome extraction can be compressed from r stabilizer measurements to O(d log r) by combining stabilizer generators through the parity check matrix of a classical code.

  2. Real-time adaptive quantum error correction by model-free multi-agent learning

    quant-ph 2025-09 conditional novelty 7.0 of 10

    Adaptive quantum error correction: multi-agent RL discovers QEC circuits offline; a bandit-controlled variational layer retrains online, cutting logical infidelity about 18x (qubit) and 3x (qutrit) under drifting bit/...

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