QUANTUM CODES WITH IMPROVED MINIMUM DISTANCE

Keqin Feng

Manabu Hagiwara

Ruihu Li, Xueliang Li, Zongben Xu

We give elementary recursive constructions of quaternary self-orthogonal codes with dual distance three for all n ≥ 5. Consequently, good linear quantum codes of minimum distance three for such length n are obtained. Almost all of these linear quantum codes are optimal or near optimal.

Carlos Galindo, Fernando Hernando, Diego Ruano

Jian Liu

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.

Hao Chen