Codes and designs
Codes and designs
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DOI：
10.1007/978-94-010-1220-1_16
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
J. H. Lint
中科院分区：
文献类型：
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作者：
J. H. Lint
我们用V（n，q）表示来自q符号字母表F（Le. V（n，q）= IFn）。如果q是素数幂，我们取IF= IF q，并将V（n，q）解释为IF上的n维向量空间。V（n，q）的元素称为字（或向量），并由下划线符号表示。（0，0，···，0）这个词用e表示。两个词~和Z的（汉明）距离d（~，Z）由d（~，Z）定义：=+ r {i I lsi sn，xi~ Yi}·词~的权重w（~）是d（~，ε）。V（n，q）的子集C称为码。我们说C是e-纠错的，如果对~ E C，Z E C，有~ Z，d（~，Z）~ 2 e + 1。C的最小距离，由d定义：min {d（~，z）I~ c，Z ~ c，Z ~ c}确定码的纠错能力集合Se（~）：={Z€ V（n，q）I d（~，Z）se}称为围绕~的半径为e的球面。如果球面的集合Se（~ n，其中~ n贯穿C，形成V（n，q）的划分，则C被称为a
We denote by V (n, q) the set of all n-tuples from a q-symbol alphabetF (Le. V (n, q)= lFn). If q is a prime power we take IF= IF q and interpret V (n, q) as n-dimensional vector space over IF• In q any case we distinguish an element of IF and denote it by O. The elements of V (n, q) are called words (or vectors) and are denoted by underlined symbols. The word (0, 0,•••, 0) is denoted by£. The (Hamming) distance d (~, Z) of two words~ and Z is defined by d (~, Z):=+ r {i I lsi sn, xi~ Yi}•The weight w (~) of the word~ is d (~,£). A subset C of V (n, q) is called a code. We say that C is e-error-correcting if d (~, Z)~ 2e+ 1 for all pairs~ E C, Z E C, with~~ Z. The minimum distance of C, defined by d:.. min {d (~, z) I~€ c, Z€ C,~"'Z} determines the error correcting capability e:= Ld; l J of the code. The set Se (~):={Z€ V (n, q) I d (~, Z) se} is called the sphere of radius e around~. If the set of spheres Se (~)'where~ runs through C, forms a partition of V (n, q) then C is called a