Abstract
Based on finite field and combinatorics theory, an elementary recursive construction is used to construct Hermitian self-orthogonal codes over 𝔽9, the Galois field with nine elements, with dual distance three for all n ≥ 4. Consequently, good ternary linear quantum codes of minimum distance three for such length n are obtained. These ternary linear quantum codes are optimal or near optimal according to the quantum Singleton bound and quantum Hamming bound.
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