Optimal Binary Self-orthogonal Codes
WANG Wei-liang
FAN Yang-yu
KOU Guang-xing
YAN Long
Abstract：Designing general binary self-orthogonal codes is a difficult problem in both classical coding theo-ry and quantum coding theory.The structure of one-generator quasi-cyclic codes constructed by concatena-ting binary circulant matrices is investigated.Twenty-eight optimal or best known binary self-orthogonal codes are built by designing the structure of a special subclass of quasi-cyclic codes,which takes advantage of some restrictions such as the shifting equivalence relation on vector,the equivalence relation on linear codes and even weight property of binary self-orthogonal codes.A puncturing-expurgating construction method for binary self-orthogonal codes is proposed,and sixty-two derived codes from these obtained self-orthogonal codes are constructed.In comparison with Literature (13),67 and 23 among our ninety self-orthogonal codes are separately optimal and best known.The construction results indicate that these two methods are effective to design general self-orthogonal codes.Furthermore,the ideas can preferably solve the construction problem of self-orthogonal codes with possible larger minimum dual weight,which is the critical infrastructure in designing better quantum codes.
Keywords：linear codeself-orthogonal codequasi-cyclic codepuncturing-expurgating construction
Publication Date：2015-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：4( 85-88 )