Construction of S-chains From Self-dual Codes
Qiu Dang-qing · Journal of Air Force Engineering University · 2008
It is a central problem in the research of coding to study the existence,structure and construction of the certain optimal property codes.In order to construct the quantum error-correcting codes,people have begun to study the self-orthogonal code that has the special self-dual distance.In this paper,two classes of sub-codes,which have optimal dual distance or intended optimal dual distance,of the binary non-decomposable self-dual codes of length n between 12 and 20,such as B12,D14,E16,F16,H18,I18,J20,K20,L20,M20 and S20,and the corresponding S-chain construction are studied.Based on the generator matrices of the self-dual codes,optimal sub-codes of dual distance 2,3 and 4 of these self-dual codes are constructed by using a combinational method.Then code chains of these optimal sub-codes and their dual codes are discussed.Consequently,S-chains are constructed from these sub-codes with optimal dual distance or intended optimal dual distance.Finally,some very good quantum error-correcting codes are constructed from the S-chains obtained.These quantum codes are the ones that the distance reaches the maximum when their n and k are given.