Flag-transitive point-primitive 2-(v,k,4) symmetric designs and two dimensional classical groups

Let D be a 2-（v, k, 4） symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ≥G ≤Aut（X） where X ≌ PSL2（q）.Then D is a 2-（15,8,4） symmetric design with X = PSL2（9） and Xx = PGL2（3） where x is a point of D.

Secret Sharing Schemes Based on the Dual Code of the Code of a Symmetric （v, k, λ）-Design and Minimal Access Sets

Secret sharing has been a subject of study for over 30 years. The coding theory has been an important role in the constructing of the secret sharing schemes. It is known that every linear code can be used to construct the secret sharing schemes. Since the code of a symmetric （V, k, λ）-design is a linear code, this study is about the secret sharing schemes based on C of Fp-code C of asymmetric （v, k, λ）-design.

CONSTRUCTION OF NONSYSTEMATIC LOW-DENSITY PARITY-CHECK CODES BASED ON SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGN

This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.

Some Construction Methods of Optimum Chemical Balance Weighing Designs III

Methods of constructing the optimum chemical balance weighing designs from symmetric balanced incomplete block designs are proposed with illustration. As a by-product pairwise efficiency and variance balanced designs are also obtained.

Symmetrical periods used as matching layers in multilayer thin film design

Properties of symmetrical layers as matching layers in multilayer thin film design were analyzed. A calculation method was presented to derive parameters of desired equivalent refractive index. A harmonic beam splitter was designed and fabricated to test this matching method. OCIS codes： 230.1360, 220.0220, 310.6860.

A Relationship Between the Weight Enumerators and Minimal Codewords

In this paper using the weight enumerators of a linear [n, k]--code, we give a theorem about minimal codewords. In this n context, we show that while 1 E C if Wmin〉 n/2 in the binary [n, k] --code C, then all of the nonzero codewords of C are 2 minimal. Therefore, we obtain a corollary.

Flag-transitive 2-（v, k, λ） symmetric designs with （k, λ） =1 and alternating socle

Consider the flag-transitive 2-（v, k, λ） symmetric designs with （k, λ）= 1. We prove that if （） is a nontrivial 2-（v, k, λ）symmetric design with （k,λ） = 1 and G ≤ Aut（） is flag-transitive with Sot（G） = An for n ≥5, then is the projective space PG2（3, 2） and G = A7.

Sporadic groups and flag-transitive triplanes

Let D be a triplane, i.e., a 2-(ν, k, 3) symmetric design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G is flag-transitive point-primitive, then the socle of G cannot be a sporadic simple group.

Affine groups and flag-transitive triplanes

Let D be a nontrivial 2-(v, k, 3) symmetric design (triplane) and let G≤Aut(D) be flag-transitive and point-primitive. In this paper, we prove that if G is an affine group, then G≤AΓL1(q), where q is some power of a prime p and p≥5.