Weight Calculation And Purity Identification Of Symplectic Self-orthogonal Codes
Kai Cao, Luobin Guo, Chaoyang Li, Yuxiang Zheng, Leinan He, Zhenpeng Zhao · Advances in intelligent systems research/Advances in Intelligent Systems Research · 2014
The purity identification of quantum errorcorrecting codes and symplectic self-orthogonal is a pivotal problem in quantum code theory.This work is dedicated to some issues of symplectic codes.First, by the MacWillams identity, a fast algorithm to determine the weight polynomial of high-dimension symplectic codes is designed; second a solution to seek for the dual codes of symplectic codes is derived; third the effective method to identify the purity of symplectic codes is obtained; and at last constructions of symplectic selforthogonal codes are given, resulted three impure symplectic self-orthogonal codes, the quantum codes stabilized by the three impure symplectic self-orthogonal codes are optimal.The above work may offer new methods for purity identification of symplectic self-orthogonal codes and quantum error-correcting codes. Keywords-