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A Construction of Maximal Linearly Independent Array 被引量:2
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作者 Jun Wu DONG Xue Li WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第7期1331-1344,共14页
Let M be a subset of r-dimensional vector space Vτ (F2) over a finite field F2, consisting of n nonzero vectors, such that every t vectors of M are linearly independent over F2. Then M is called (n, t)-linearly i... Let M be a subset of r-dimensional vector space Vτ (F2) over a finite field F2, consisting of n nonzero vectors, such that every t vectors of M are linearly independent over F2. Then M is called (n, t)-linearly independent array of length n over Vτ(F2). The (n, t)-linearly independent array M that has the maximal number of elements is called the maximal (r, t)-linearly independent array, and the maximal number is denoted by M(r, t). It is an interesting combinatorial structure, which has many applications in cryptography and coding theory. It can be used to construct orthogonal arrays, strong partial balanced designs. It can also be used to design good linear codes, In this paper, we construct a class of maximal (r, t)-linearly independent arrays of length r + 2, and provide some enumerator theorems. 展开更多
关键词 maximal linearly independent array orthogonal array hamming weight
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