论文标题
使用LFSR序列有序的正交阵列构造
Ordered Orthogonal Array Construction Using LFSR Sequences
论文作者
论文摘要
我们提出了使用线性反馈移位寄存器序列（LFSRS）的有限字段$ \ mathbb {f} _ {q} $的新构造的强度$ t $的正交阵列（OOA），并带有$（q + 1）t $列。 ooas自然与$（t，m，s）$ - 网络，线性代码和MDS代码相关。我们的构造从所有长度$ \ frac {q^{t} -1} {q-1} $的LFSR序列的$ \ frac {q^{q^{q^{q^{q^{q^{q^{q^{q^{q^{q^{q^{q-1} $中选择合适的列的LFSR序列生成的原始多项式$ $ t $ a $ $ t $生成的LFSR序列。我们证明了关于LFSR中运行的相对位置的属性，该位置保证了构造的OOA具有强度$ t $。我们OOA的一组参数与Rosenbloom和Tsfasman（1997）和Skriganov（2002）给出的参数相同，但是构造的阵列不同。我们在实验上验证了我们的OOA比Rosenbloom-Tsfasman-Skriganov Ooas强，因为我们的OOA更接近“完整”正交阵列。我们还讨论了我们的OOA构造与以前的技术相关联，从$ \ mathbb {f} _ {q} $以及超刻法同构的一组线性独立向量构建OOA。
We present a new construction of ordered orthogonal arrays (OOA) of strength $t$ with $(q + 1)t$ columns over a finite field $\mathbb{F}_{q}$ using linear feedback shift register sequences (LFSRs). OOAs are naturally related to $(t, m, s)$-nets, linear codes, and MDS codes. Our construction selects suitable columns from the array formed by all subintervals of length $\frac{q^{t}-1}{q-1}$ of an LFSR sequence generated by a primitive polynomial of degree $t$ over $\mathbb{F}_{q}$. We prove properties about the relative positions of runs in an LFSR which guarantee that the constructed OOA has strength $t$. The set of parameters of our OOAs are the same as the ones given by Rosenbloom and Tsfasman (1997) and Skriganov (2002), but the constructed arrays are different. We experimentally verify that our OOAs are stronger than the Rosenbloom-Tsfasman-Skriganov OOAs in the sense that ours are "closer" to being a "full" orthogonal array. We also discuss how our OOA construction relates to previous techniques to build OOAs from a set of linearly independent vectors over $\mathbb{F}_{q}$, as well as to hypergraph homomorphisms.
