A Note on Quantum Hamming Bound
Salah A. Aly
TL;DR
This paper proves the quantum Hamming bound for a specific class of quantum error-correcting codes and calculates the maximum lengths of certain MDS stabilizer codes, advancing understanding in quantum coding theory.
Contribution
It establishes the quantum Hamming bound for double error-correcting degenerate stabilizer codes and determines maximum lengths of MDS stabilizer codes.
Findings
Quantum Hamming bound proven for double error-correcting degenerate stabilizer codes.
Maximum length of single and double error-correcting MDS stabilizer codes computed.
Advances in quantum coding theory understanding.
Abstract
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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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Quantum-Dot Cellular Automata