New classes of 2-weight cyclic codes

We introduce new classes of 2-weight cyclic codes which are direct sums of 1-weight irreducible cyclic codes      

Co-Orthogonal Codes

We define, construct and sketch possible applications of a new class of non-linear codes: co-orthogonal codes, with possible applications in cryptography and parallel processing. We also describe a fast and general method for generating (non-linear) codes with prescribed dot-products with the help of multi-linear polynomials.     

最优带仲裁认证码

本文研究带仲裁认证码（亦称A^2-码）。一个A^2-码，当它的欺骗攻击成功概率达到信息论下界且密钥长度也达到最小时称为是最优的。本文给出最优A^2-码的组合结构的特征，从而将构造最优A^2-码的问题归结为构造相应的一类组合设计的问题。     

Summing the derivative expansion of the effective action

The derivative expansion of the effective action is a perturbative development in derivatives of the fields. The expansion breaks down when some of the derivatives are too large. We show how to sum exactly the first and second derivatives and treat perturbatively derivatives higher than second.     

广义准正则格形码距离谱的计算

本文讨论了格形码距离谱的计算问题，定义了度量空间意义下的广义准正则格形码，对具有Ｉｍａｉ与Ｈｉｒａｋａｗａ［２］和Ｕｎｇｅｒｂｏｅｃｋ［３］定义的典型的时不变网格结构的广义准正则格形码，证明了其距离谱可用全零信息序列对应的码字进行计算。在理论上推广了Ｍ．Ｒｏｕａｎｃｅ与Ｄ．Ｊ．Ｃｏｓｔｅｌｏ的结果，解决了非平方欧几里德度量意义下一类ＴＣＭ信号序列的距离谱计算问题     

The minimum squared euclidean distance of multi-h phase codes

The minimum squared Euclidean distance(MSED) of binary multi-h phase codes is presented. The signal segregation degree(SSD) has been put forward to determine MSED of multi-h phase codes. In order to maximize MSED, SSD should be as large as possible. The necessary and sufficient conditions of maximizing SSD are derived. Finally, SSD and the exact formulae for MSED of binary 2-h phase codes are also presented.     

Skeleton chain coding for Chinese characters

The compression of Chinese characters is very important for Chinese office automation and desktop publishing. In this paper, various methods are used to compress 13,051 Chinese characters losslessly by coding their skeleton points. The skeleton points are composed of isolated points and curves. To trace every point in a curve once and consecutively is a NP problem. Therefore, we use contour path following and revisiting algorithms to trace skeleton curves with chain codes. The remaining isolated skeleton points are encoded by an Elias code. Our coding method has a better compression rate than that of conventional skeleton coding.     

A Two-Level Spreading-despreading CDMA System and Its Performance Evaluation

1　IntroductionHowtosuppresstheinterferenceintheCDMAsystems,includingtheSelfInterference(SI) ,Mul tipleAccessInterference(MAI)andtheAdjacentCellInterference(ACI) ,isthekeypointinimprov ingthesystemperformanceandcapacity .Insteadofthecomplicatedspecializedsignalprocessingtech niquesusedbefore[1～ 4] ,spreadingsequenceswithgoodcorrelationpropertiescanimprovethesystemperformanceradically[5] .InRef.[6～ 9],theconceptofZeroCorrelationZone (ZCZ) ,whichisequivalenttothegeneralizedothogonal…     

Degrevlex Gröbner bases of generic complete intersections

In this paper, we study the Hilbert–Samuel function of a generic standard graded K-algebra

K[X₁,…,X_n]/(g₁,…,g_m)

when refined by an (ℓ)-adic filtration, ℓ being a linear form. From this we obtain a structure theorem which describes the stairs of a generic complete intersection for the degree-reverse-lexicographic order. We show what this means for generic standard (or Gröbner) bases for this order; in particular, we consider an “orderly filling up” conjecture, and we propose a strategy for the standard basis algorithm which could be useful in generic-like cases.     

Constructing two-weight codes with prescribed groups of automorphisms

We construct new linear two-weight codes over the finite field with q elements. To do so we solve the equivalent problem of finding point sets in the projective geometry with certain intersection properties. These point sets are in bijection to solutions of a Diophantine linear system of equations. To reduce the size of the system of equations we restrict the search for solutions to solutions with special symmetries.Two-weight codes can be used to define strongly regular graphs. We give tables of the two-weight codes and the corresponding strongly regular graphs. In some cases we find new distance-optimal two-weight codes and also new strongly regular graphs.