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对偶距离分布
    On Dual Distance Distribution of Equidistant Codes
    等距码的对偶距离分布及其性质
    In this paper, dual distance distribution and dual weight distribution of binary con-stant weight code are discussed. First, their definitions, properties and relations are giv-en. Then, for constant weight code, a recursive equation of dual weight distribution,which implies a recursive inequality of dual distance distribution, is obtained.
    本文讨论了二元等重码的对偶距离分布和对偶重量分布.首先给出了二元码的对偶重量分布和对偶距离分布的定义、性质和关系,然后对等重码,导出了其对偶重量分布的一个递推关系式,以此得到了对偶距离分布的一个递推不等式.最后,讨论了上述分布的一些应用.
    By using the properties of dual distance distribution,the necessary condition ofis proved to be also sufficient for δ =1.Moreover,we have that for ( n,2,ω )code,being proper is equivalent to being good.
    本文利用对偶距离分布的性质,从理论上证明了文[4]的必要条件在δ=1时实际上是充要条件,并得出对于(n,2,w)码,最佳检错码与检错好码是等价的;
    By using the dual distance distribution and its properties for binary code C withlength n and number of codewords M, the Althofer-Sillke inequality is improved when Misodd. The exact values of minimum average Hamming distance of C are determined when Mequals 2n-1 or 2n-1 -1.
    通过对二元n长码C的对偶距离分布的研究,在码字数为奇数的情况下,改进了Al-thofer-Sillke[1]和[2]文关于C的码字间平均Hamming距离及其均方差的不等式,并在码字数为2n-1或2n-1-1时,确定了码C的最小平均距离及其均方差的精确值.
    In this paper,By definition δ(x_i,y_i) function,Binary weights (n,2,ω_1,ω_2) codes is generalized to q-ary weights(n,2,ω_1,ω_2) codes,Be based on distance distribution and Dual distance distribution of codes,to discuss several condition of the code being proper code.
    通过定义δ(xi,yi)函数,把2元非线性2-重量码(n,2,ω1,ω2)的性质推广到q元非线性2-重量码(n,2,ω1,ω2)上,根据码的距离分布和对偶距离分布讨论了码C的不可检错概率. 给出了码C不是最佳检错码的几个条件.
    Firstly,by using the dual distance distribution and its properties for BCWC,we obtain a new lower bound of UEP for BCWC which improves the best known corresponding results by Fu-Klve-Wei.
    首先,我们通过研究二元等重码的对偶距离分布及其性质,给出二元等重码UEP的一个新的下界,该下界改进了Fu-K lve-W ei的最新结果;
 

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