代数几何码的译码算法研究

Algebriac-geometric codes are very important in the theory of error-correcting codes because of its theretical and potential application value. We studied the error-correcting capability and deconding of algebraic-geometric codes in this project, including the following topics: improvement of error-correcting capability of Hermitian codes, the minimum distances of Schubert codes and the application of algebraic-geometric codes in the construction of quantum error-correcting codes. We constructed a sequence of asymptotically good quantum error-correcting codes and improved the ALT bound.

本课题研究代数几何码已有的译码法，尤其是冯拉欧译码法，对具好的性质的代数几何码，如欧梅特码，嘎西--斯梯奇努兹曲线上的渐进好码的译码能力，如译码法的纠错个数的严格确定，对超冯拉欧界的错型的处理能力等，也寻找对好码的更有效，可处理更多错误的译码法，本课题对具潜在应用价值的代数几何码的可能技术应用有意义。