On the Hamming distances of repeated-root constacyclic codes of length 4ps

Let $p$ be an odd prime, $s$, $m$ be positive integers, $\gamma ,\lambda$ be nonzero elements of the finite field ${\mathbb{F}}_{p^m}$ such that ${\gamma }^{p^s}=\lambda$. In this paper, we show that, for any positive integer $\eta$, the Hamming distances of all repeated-root $\lambda$-constacyclic codes of length $\eta p^s$ can be determined by those of certain simple-root $\gamma$-constacyclic codes of length $\eta$. Using this result, Hamming distances of all constacyclic codes of length $4p^s$ are obtained. As an application, we identify all MDS $\lambda$-constacyclic codes of length $4p^s$.     

The dual code of any (δ+αu2)-constacyclic code over F2m[u]∕〈u4〉 of oddly even length

Let ${\mathbb{F}}_{2^m}$ be a finite field of cardinality $2^m$, $R={\mathbb{F}}_{2^m}\left[u\right]∕〈u^4〉={\mathbb{F}}_{2^m}+u{\mathbb{F}}_{2^m}+u^2{\mathbb{F}}_{2^m}+u^3{\mathbb{F}}_{2^m}$ $(u^4=0)$ which is a finite chain ring, and $n$ is an odd positive integer. For any $\delta ,\alpha \in {\mathbb{F}}_{2^m}^{\times }$, an explicit representation for the dual code of any $(\delta +\alpha u^2)$-constacyclic code over $R$ of length $2n$ is given. And some dual codes of $(1+u^2)$-constacyclic codes over $R$ of length 14 are constructed. For the case of $\delta =1$, all distinct self-dual $(1+\alpha u^2)$-constacyclic codes over $R$ of length $2n$ are determined.     

Gray codes extending quadratic matchings

Is it true that every matching in the n-dimensional hypercube can be extended to a Gray code? More than two decades have passed since Ruskey and Savage asked this question and the problem still remains open. A solution is known only in some special cases, including perfect matchings or matchings of linear size. This article shows that the answer to the Ruskey–Savage problem is affirmative for every matching of size at most . The proof is based on an inductive construction that extends balanced matchings in the completion of the hypercube by edges of into a Hamilton cycle of . On the other hand, we show that for every there is a balanced matching in of size that cannot be extended in this way.     

Linear codes associated to skew-symmetric determinantal varieties

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these codes is given.     

虚拟解法分析浸入边界法的精度

浸入边界法是对流固耦合系统进行建模和模拟的有效工具,在生物力学领域的应用尤为广泛．该文的工作主要包含两个部分:程序验证和精度分析．前者证明了程序的正确性,后者给出了浸入边界法的精度．两部分工作均使用虚拟解法作为研究工具．在程序验证部分,使用二阶空间离散格式进行数值计算,通过分析各种变量的离散误差,得到的程序计算精度阶是二阶,与理论精度阶一致,证明了数值计算所使用程序的正确性．精度分析部分工作在此基础上展开．引入压强跳跃,在动量方程中加入相应源项,通过分析带有源项的控制方程中各物理量的离散误差,证明浸入边界法只具有一阶精度．同时可以得出以下结论:粗网格无法敏感地捕捉浸入边界的影响;当Euler网格固定时,增加Lagrange标志点的数目并不会改善计算误差．     

沿齐次曲线的强奇异积分算子在调幅空间上的有界性

设Γ_θ(t)为R~n(n≥2)中的齐次曲线,定义沿齐次曲线的强奇异积分算子T_(n,α,β)f(x)=p.v.∫_(-1)~1f(x-Γ_θ(t))(e~((-2πi|t|)~(-β))/(t|t|~α))dt,α,β>0.本文讨论了上述奇异积分算子在广义调幅空间上的有界性.     

The depth spectrums of constacyclic codes over finite chain rings

In light of the generator polynomials of constacyclic codes over finite chain rings, the depth spectrum of constacyclic codes can be determined if (n,p)=1$(n,p)=1$.