Binary construction of quantum codes of minimum distance three and four

Authors:
Ruihu Li;Xueliang Li
Affiliations:
Dept. of Appl. Math. & Phys., Air Force Eng. Univ., Shaanxi, China;-
Venue:
IEEE Transactions on Information Theory
Year:
2004

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Abstract

We give elementary recursive constructions of binary self-orthogonal codes with dual distance four for all even lengths n≥12 and n=8. Consequently, good quantum codes of minimum distance three and four for such length n are obtained via Steane's construction and the CSS construction. Previously, such quantum codes were explicitly constructed only for a sparse set of lengths. Almost all of our quantum codes of minimum distance three are optimal or near optimal, and some of our minimum-distance four quantum codes are better than or comparable with those known before.