Self-orthogonal codes with dual distance three and quantum codes with distance three over $$\mathbb F _5$$F5

• Authors: Fangchi Liang
• Venue: Quantum Information Processing
• Year: 2013

Self-orthogonal codes with dual distance three and quantum codes with distance three constructed from self-orthogonal codes over $$\mathbb F _5$$ F 5 are discussed in this paper. Firstly, for given code length $$n\ge 5$$ n 驴 5 , a $$[n,k]_{5}$$ [ n , k ] 5 self-orthogonal code with minimal dimension $$k$$ k and dual distance three is constructed. Secondly, for each $$n\ge 5$$ n 驴 5 , two nested self-orthogonal codes with dual distance two and three are constructed, and consequently quantum code of length $$n$$ n and distance three is constructed via Steane construction. All of these quantum codes constructed via Steane construction are optimal or near optimal according to the quantum Hamming bound.