【摘要】 广义汉明重量是线性码的最小距离的自然推广,它在McEliece公开密钥体制中有应用.文献[1]给出了二元[n,2]线性码的广义汉明重量谱的计数方法,但该计数公式只适于d2≥2d1时的特殊情形.本文深入分析了q元线性码的生成特征,不仅得到了q元[n,2]线性码的广义汉明重量谱的完备计数公式,而且得到了q=2时的计数公式.因此,本文进一步补充和推广了文献[1]中的结论,该结论对线性码的广义汉明重量的理论研究和实际计算是有重要意义.更多还原

【Abstract】 Generalized Hamming Weights are natural generalizations of the minimum distances of linear codes.They have an important application in McEliece public key cryptosystems.Luo Shou-shang and et al gave the numeration of Generalized Hamming Weights for binary linear codes in [1].But the expression of the numeration has been found to be useful in the special condition when d2≥2d1.In this paper,we further analyse the generator matrix of the linear codes on the field Fq,and we not only obtain the perfect result of the Generalized Hamming Weights for linear codes on the field Fq,but also get the special result when q is equal to 2.Therefor our result is a generalization of the result of the paper [1].And it also play an important role for theoretical study and calculation of the Generalized Hamming Weights for linear codes.更多还原