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It is unknown whether or not there exists an [87, 5, 57; 3]-code. Such a code would meet the Griesmer bound. The purpose of this paper is to give a constructive proof of the existence of [q
4 + q
2 – q, 5, q
4 – q
3 + q
2 – 2q; q]-codes for any prime power q 3. As a special case, it is shown that there exists an [87, 5, 57; 3]-code with weight enumerator 1 + 156z
37 + 82z
60 + 2z
63 + 2z
78. The new construction settles an open problem due to Hill and Newton [10]. 相似文献
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Shaun Cooper 《The Ramanujan Journal》2009,20(3):311-328
In both his second and lost notebooks, Ramanujan introduced a function, related to the Rogers–Ramanujan continued fraction
and its quadratic transformation, and listed several of its properties. We extend these results and develop a systematic theory. 相似文献
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§1 引言 M.D.Atkinson在文[3]中提出一个猜想:若G是Ω上2—传递而非2—本原置换群,则G是下面四种群之一: ⅰ) 素数P级P(P-1)阶亚循环群; ⅱ) 对于素数P,是2~P级2~P(2~P-1)或2~P(2~P-1)P阶群; ⅲ) 是有λ=1的区组设计的自同构群; ⅳ) Sz(q)≤G≤Aut(Sz(q)) 相似文献
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In [ 3 ] M. D. Atkinson conjectured that if G is a doubly transitive but not doubly primitive permutation group on Ω, then G is of one of the following four types: i) Metacyclic groups of prime degree p and of order p(p -1); ii) Groups of degree 2p and of order 2p(2p-1)or 2p(2p-l)p for some prime p;iii)Gr-oups of automorphisms of a block design with λ=1; iv) Sz(q)≤G≤Aut(Sz(g)).In this paper we proved this conjecture in a special case without using the result of classification of finte simple groups, Qur explicit result is as follows: Theorem. Let G be a doubly transitive group on set Ω,where |Ω|=6q+1 and q is a prime, then one of the following holds: i)G is doubly primitive on Ω;ii) G is sharply doubly transitive on Ω; iii) G is a groups of automorphisms of a block design with λ=1. 相似文献
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设{u_k}_k≥0为一个线性递归序列.序列{u_k(mod q)}_(k≥0)是周期的,很多人都对其周期有过研究.本文应用二次数域中理想的理论,较完全地刻面了二次线性递归序列模q的周期长度,所获结果加强并推广了Engstrom及Wall的结论. 相似文献
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问 在求解与等比数列有关的问题时 ,我们常常忘了您 (指公比 q)的讨论 ,请问用什么方法来强化这种讨论意识 ?答 忽视讨论 ,实际上是忽视了引进分类讨论的因素分析 ,我的分类讨论的原因通常是由求和公式成立的条件而引起的 ,所以 ,我建议同学们平时多看看课本中求前n项和公式、求所有项和公式的推导过程 ,多想想过程中的附加条件 ,并且亲自推导推导 ,这样在解题时 ,只要一用到这些公式 ,就会自然地想起过程 ,从而激发自己的讨论意识 .问 那么在讨论时 ,怎样分类 ,分几类呢 ?答 分类讨论是按照一定的标准 ,把数学对象划分为不同种类分别… 相似文献
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The Ramanujan Journal - Recently, Andrews, Dixit, and Yee defined two partition functions $$p_{\omega }(n)$$ and $$p_{\nu }(n)$$ that are related with Ramanujan’s mock theta functions... 相似文献
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In the “lost notebook”, Ramanujan recorded infinite product expansions for
$\frac{1}
{{\sqrt r }} - \left( {\frac{{1 - \sqrt 5 }}
{2}} \right)\sqrt r and \frac{1}
{{\sqrt r }} - \left( {\frac{{1 + \sqrt 5 }}
{2}} \right)\sqrt r ,$\frac{1}
{{\sqrt r }} - \left( {\frac{{1 - \sqrt 5 }}
{2}} \right)\sqrt r and \frac{1}
{{\sqrt r }} - \left( {\frac{{1 + \sqrt 5 }}
{2}} \right)\sqrt r , 相似文献
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An interpolation method is introduced for anisotropic spaces which generalizes the method by D. L. Fernandez [4]. By means of this method, interpolation properties of Besov B pτ σq and Lizorkin-Triebel F pτ σq spaces are investigated. Among others, the completeness of the scale of these spaces is proved with respect to the considered interpolation method. 相似文献
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Let be a finite group and let be the set of all complex irreducible character degrees of . Bertram Huppert conjectured that if is a finite nonAbelian simple group such that , then , where is an Abelian group. In this paper, we verify the conjecture for the family of simple exceptional groups of Lie type for . 相似文献
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Journal of Geometry - 相似文献
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If (O) is a quadratic cone in PG(3,q), with vertex x, then a flock of (O) is a partition of (O)-{x} into q disjoint conics. With such a flock there correspond a translation plane of order q
2 and a generalized quadrangle of order (q
2, q). Here we determine all flocks of (O) for q 8. 相似文献
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Let G be a finite group and cd(G) be the set of all complex irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G???H × A, where A is an abelian group. In this paper, we verify the conjecture for the family of simple exceptional groups of Lie type 3 D 4(q), when q?≥?3. 相似文献
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不等式ap+q+bp+q≥apbq+aqbp的应用钟成圣(安徽省合肥市中国科大附中230026)定理若a,b,p,q∈R+,则ap+q+bp+q≥apbq+aqbp①当且仅当a=b时等号成立.证∵p,q∈R+,∴幂函数y=xp和y=xq在(0,+∞)... 相似文献
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