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Home - Research - Research Highlights

刘子辉老师在编码理论的研究方面取得新进展

发布时间:2012-09-03
  最近,数学与统计学院刘子辉老师与其合作者在编码理论的研究方面取得了一些新成果,他们在《New code equivalence based on relative generalized Hamming weights》一文中,他们利用有限射影几何中子空间的计数方法,把MacWilliams 定理中通过利用码字的最小重量给出码的等价的思想方法推广到利用一类子码的支撑重量判别码的等价,使得MacWilliams 判别方法成为当前给出的判别方法的一个小的特例。

  码的等价是编码理论中经典又困难的研究课题。等价的码拥有相同的广义汉明重量和其他重要的码的参数,基于此,码的等价是作为码分类的基础。码的等价和码的等价判别方法吸引了众多的编码学者。编码理论中著名的MacWillams 定理给出了码等价的一个判别方法,以密西根大学数学系主任Wood 教授为代表的学者利用群特征标理论给出了MacWilliams 定理的新证明,他们还把MacWilliams 定理推广到环上,尤其是最近,他们证明了码的等价可以反过来等价地刻划Frobenius 有限环,而Frobenius 环在群表示理论、代数几何、数论中有重要应用。上述工作使得码的等价判别方法的寻找既有理论意义,又有应用价值。

  刘子辉老师的工作得到审稿人的很好评价,三位审稿人一致认为此判别法广泛推广了MacWilliams定理,判别方法新颖,证明构思巧妙。文章结果发表在信息和编码方向权威杂志《Information Sciences》(Vol. 181, No.19, 2011, pp. 4309-4317)上。

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