有序码与正交表的界

Ordered Covering Arrays and Upper Bounds on Covering Codes in NRT spaces

This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also obtained by improving a general upper bound. We explore the connection between ordered covering arrays and covering codes in NRT spaces, which generalize similar results for the Hamming metric. Combining the new upper bounds for covering codes in NRT spaces and ordered covering arrays, we improve upper bounds on covering codes in NRT spaces for larger alphabets.…

Bounds on Covering Codes in RT spaces using Ordered Covering Arrays

In this work, constructions of ordered covering arrays are discussed and applied to obtain new upper bounds on covering codes in Rosenbloom-Tsfasman spaces (RT spaces), improving or extending some previous results.

Ordered Orthogonal Array Construction Using LFSR Sequences

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 str…

n次正交表的格

The Lattice of N-Run Orthogonal Arrays

如果指定了强度为2的（混合水平）正交数组中的运行游程数，则可能有多少水平和因子？具有N次运行的正交表的可能参数集的集合具有自然的晶格结构，这是由“扩展的构造”方法引起的。特别是在这个晶格中的对偶原子是最重要的参数集，因为任何其他参数集的N运行正交阵列可以构造从他们。为了了解对偶原子的数量，并开始理解晶格作为N的函数，我们研究晶格的高度和大小。结果表明，该系统的高度至多为[c（N-1）]，其中c= 1.4039.并且存在N的值的无穷序列，对于该序列，达到该界。另一方面，格中的节点数由N的超多项式函数限定（对于N的某些值序列，超多项式增长确实会发生）。使用基于"混合分布“的新构造，确定了具有64次运行的所有参数集。其中四个64运行正交表似乎是新的。

正交拉丁立方对的构造

Constructions of Pairs of Orthogonal Latin Cubes

一对$q$阶的正交拉丁立方体等价于具有距离$3$的MDS码或等价于${\rm OA}_1(3,5,q)$正交阵列。我们构造了一个序列的正交拉丁立方体对以前未知的订单$q_i=16(18i-1)+4$和$q'_i=16(18i+5)+4$。正交表的最小新获得的参数是${\rm OA}_1(3,5,84)$。关键词：拉丁方，拉丁立方体，MOLS，MDS码，区组设计，Steiner系统，正交表

$Z_4$ -码及其作为正交阵列的Gray映射图像

$Z_4$-codes and their Gray map images as orthogonal arrays

Delsarte的一个经典结果将线性码的强度（作为正交数组）与其对偶的最小重量联系起来：前者比后者小小于。我们表明，Delsarte的观察扩展到任意有限环的代码。自从Hammons的\emph{et al.}的论文发表以来，环上的码，特别是$Z_4$上的码及其二进制Gray映射像引起了人们的极大兴趣。我们表明，Delsarte的观察扩展到代码在任意有限交换环单位元。此外，我们表明，一个$Z_4$码的灰度图图像的强度是一个小于的最小李重量的灰度图图像。