激光聚变中的科学计算

科学计算在激光聚变研究中发挥着重要的作用.经过长期的努力,中国已形成了以LARED系列程序为核心的分段模拟激光聚变主要环节和关键问题的二维数值模拟能力.文章首先介绍了激光聚变的主要物理过程、主要物理过程的特征以及对科学计算的要求.其次,介绍了LARED系列程序的主要功能以及在激光聚变物理研究中的应用,介绍了正在研制和发展的模拟激光聚变全过程的新一代高性能并行应用程序的思路.最后,介绍了激光聚变科学计算中面临的一些挑战性问题.     

Intersections of q-ary perfect codes

The intersections of q-ary perfect codes are under study. We prove that there exist two q-ary perfect codes C ₁ and C ₂ of length N = qn + 1 such that |C ₁ ? C ₂| = k · |P _i |/p for each k ∈ {0,..., p · K ? 2, p · K}, where q = p ^r , p is prime, r ≥ 1, $n = \tfrac{{q^{m - 1} - 1}}{{q - 1}}$ , m ≥ 2, |P _i | = p ^nr(q?2)+n , and K = p ^{n(2r?1)?r(m?1)}. We show also that there exist two q-ary perfect codes of length N which are intersected by p ^nr(q?3)+n codewords.     

Skew codes of prescribed distance or rank

In this paper we generalize the notion of cyclic code and construct codes as ideals in finite quotients of non-commutative polynomial rings, so called skew polynomial rings of automorphism type. We propose a method to construct block codes of prescribed rank and a method to construct block codes of prescribed distance. Since there is no unique factorization in skew polynomial rings, there are much more ideals and therefore much more codes than in the commutative case. In particular we obtain a [40, 23, 10]₄ code by imposing a distance and a [42,14,21]₈ code by imposing a rank, which both improve by one the minimum distance of the previously best known linear codes of equal length and dimension over those fields. There is a strong connection with linear difference operators and with linearized polynomials (or q-polynomials) reviewed in the first section.      

Generalized MacWilliams identities and their applications to perfect binary codes

We present generalized MacWilliams identities for binary codes. These identities naturally lead to the concepts of the local weight distribution of a binary code with respect to a word u and its MacWilliams u-transform. In the case that u is the all-one word, these ones correspond to the weight distribution of a binary code and its MacWilliams transform, respectively. We identify a word v with its support, and consider v as a subset of {1, 2,..., n}. For two words u,w of length n such that their intersection is the empty set, define the u-face centered at w to be the set . A connection between our MacWilliams u-transform and the weight distribution of a binary code in the u-face centered at the zero word is presented. As their applications, we also investigate the properties of a perfect binary code. For a perfect binary code C, the main results are as follows: first, it is proved that our local weight distribution of C is uniquely determined by the number of codewords of C in the orthogonal u-face centered at the zero word. Next, we give a direct proof for the known result, concerning the weight distribution of a coset of C in the u-face centered at the zero word, by A. Y. Vasil’eva without using induction. Finally, it is proved that the weight distribution of C in the orthogonal u-face centered at w is uniquely determined by the codewords of C in the u-face centered at the zero word.      

On the Number of k‐Dominating Independent Sets

We study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erd?s and Moser—is widely investigated, much less is known in general. In this paper we settle the question for trees and prove that the maximum number of k‐dominating independent sets in n‐vertex graphs is between and if , moreover the maximum number of 2‐dominating independent sets in n‐vertex graphs is between and . Graph constructions containing a large number of k‐dominating independent sets are coming from product graphs, complete bipartite graphs, and finite geometries. The product graph construction is associated with the number of certain Maximum Distance Separable (MDS) codes.     

Computerprogramm zur interaktiven Auswertung von 15N-tracerkinetischen Stoffwechselexperimenten

The theoretical concept of the computer program is based on the compartment theory for the 3-pool model using single pulse administration of the tracer. The code estimates the model parameters by means of the non-linear method of least squares fit under steady state conditions. Furthermore the parameters of the protein metabolism are calculated. The program works interactively and allows reading and modifying the experimental ¹⁵N tracer data via terminal and controlling the program.     

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg then the state complexity of is equal to the Wolf bound. For deg , we use Clifford's theorem to give a simple lower bound on the state complexity of . We then derive two further lower bounds on the state space dimensions of in terms of the gonality sequence of . (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.     

Existence of Perfect 4-Deletion-Correcting Codes with Length Six

By a T ^*(2, k, v)-code we mean a perfect4-deletion-correcting code of length 6 over an alphabet of size v, which is capable of correcting anycombination of up to 4 deletions and/or insertions of letters that occur in transmission of codewords. Thethird author (DCC Vol. 23, No. 1) presented a combinatorial construction for such codes and prove thata T ^*(2, 6, v)-code exists for all positive integers v 3 (mod 5), with 12 possible exceptions of v. In this paper, the notion of a directedgroup divisible quasidesign is introduced and used to show that a T ^*(2, 6,v)-code exists for all positive integers v 3 (mod 5), except possiblyfor v {173, 178, 203, 208}. The 12 missing cases for T ^*(2,6, v)-codes with v 3 (mod 5) are also provided, thereby the existenceproblem for T ^*(2, 6, v)-codes is almost complete.     

The structure of linear codes of constant weight

In this paper we determine completely the structure of linear codes over of constant weight. Namely, we determine exactly which modules underlie linear codes of constant weight, and we describe the coordinate functionals involved. The weight functions considered are: Hamming weight, Lee weight, two forms of Euclidean weight, and pre-homogeneous weights. We prove a general uniqueness theorem for virtual linear codes of constant weight. Existence is settled on a case by case basis.

     

A Characterization of Some Minihypers and its Application to Linear Codes

Any {f,r- 2+s; r,q}-minihyper includes a hyperplane in PG(r, q) if fr-1 + s 1 + q – 1 for 1 s q – 1, q 3, r 4, where i = (qi + 1 – 1)/ (q – 1 ). A lower bound on f for which an {f, r – 2 + 1; r, q}-minihyper with q 3, r 4 exists is also given. As an application to coding theory, we show the nonexistence of [ n, k, n + 1 – qk – 2 ]q codes for k 5, q 3 for qk – 1 – 2q – 1 < n qk – 1 – q – 1 when k > q – q - \sqrt q + 2$$ " align="middle" border="0"> and for when , which is a generalization of [18, Them. 2.4].