Diference Systems of Sets Based on Cosets Partitions

Difference systems of sets （DSS） are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.

An Innovative Technique for Constructing Highly Non-Linear Components of Block Cipher for Data Security against Cyber Attacks

The rapid advancement of data in web-based communication has created one of the biggest issues concerning the security of data carried over the internet from unauthorized access.To improve data security,modern cryptosystems use substitution-boxes.Nowadays,data privacy has become a key concern for consumers who transfer sensitive data from one place to another.To address these problems,many companies rely on cryptographic techniques to secure data from illegal activities and assaults.Among these cryptographic approaches,AES is a well-known algorithm that transforms plain text into cipher text by employing substitution box(S-box).The S-box disguises the relationship between cipher text and the key to guard against cipher attacks.The security of a cipher using an S-box depends on the cryptographic strength of the respective S-box.Therefore,various researchers have employed different techniques to construct high order non-linear S-box.This paper provides a novel approach for evolving S-boxes using coset graphs for the action of the alternating group A5 over the finite field and the symmetric group S256.The motivation for this work is to study the symmetric group and coset graphs.The authors have performed various analyses against conventional security criteria such as nonlinearity,differential uniformity,linear probability,the bit independence criterion,and the strict avalanche criterion to determine its high cryptographic strength.To evaluate its image application performance,the proposed S-box is also used to encrypt digital images.The performance and comparison analyses show that the suggested S-box can secure data against cyber-attacks.

Distributed Video Coding Using LDPC Codes for Wireless Video

Popular video coding standards like H.264 and MPEG working on the principle of motion-compensated pre-dictive coding demand much of the computational resources at the encoder increasing its complexity. Such bulky encoders are not suitable for applications like wireless low power surveillance, multimedia sensor networks, wireless PC cameras, mobile camera phones etc. New video coding scheme based on the principle of distributed source coding is looked upon in this paper. This scheme supports a low complexity encoder, at the same time trying to achieve the rate distortion performance of conventional video codecs. Current im-plementation uses LDPC codes for syndrome coding.

Connectivities of Minimal Cayley Coset Digraphs

we prove that the Connectivities of Minimal Cayley Coset Digraphs are their regular degrees. Connectivity of transitive digraphs and a combinatorial propertyof finite groups Ann., Discrete Math., 8 1980 61--64 Meng Jixiang and Huang Qiongxiang On the connectivity of Cayley digraphs, to appear Sabidussi, G. Vertex transitive graphs Monatsh. Math., 68 1969 426--438 Watkins, M. E. Connectivity of transitive graphs J. Combin. Theory, 8 1970 23--29 Zemor, G. On positive and negative atoms of Cayley digraphs Discrete Applied Math., 23 1989 193--195 Department of Mathematics,Xinjiang University,Urumpi 830046.APPLIED MATHEMATICS 3. Statement of Inexact Method Here we assume F to be continuousely differentiable. Inexact Newton method was first studied in the solution of smooth equations (see ). Now, such a technique has been widely used in optimizations, nonlinear complementarity problems and nonsmooth equations (see, and , etc.) In order to establish the related inexact methods,we introduce a nonlinear operator T(x): R n R n . Its components are defined as follows: (T(x)p) i=[HL(2:1,Z;2,Z] (x k+p k) i, if i∈(x k), H i(x k)+ min {(p k) i,F i(x k) Tp k}, if i∈(x k), F i(x k)+F i(x k) Tp k, i∈(x k).(3.1) Then, it is clear that the subproblem (2.5) turns to T(x k)p k=0.(3.2) In inexact algorithm, we determine p k in the followinginexact way ( see ). ‖T(x k)p k‖ υ k‖H(x k)‖,(3.3) where υ k is a given positive sequence. It is then obviously that (3.2),or equivalently (2.5), is a special case of (3.3) corresponding to υ k=0 . In particular, (3.3) can be used as a termination rule of the iterative process for solving (2.5). The following proposition shows the existence of λ k satisfying (2.4). Proposition 3.1. Let F be continuously differe ntiable. υ k is chosen so that υ k for some constant ∈(0,1). Then p k generated by (3.3) is a descent direction of θ at x k, and for some constant σ∈(0, min (1/2,1- holds θ(x k)-θ(x k+λ kp k) 2σλ kθ(x k)(3.4) for all sufficiently small λ k>0. Proof For simplification, we omit the lower subscripts k and denote (x k) i , H i(x k) , (BH(x k)p k) i , etc.by x i , H i , (BHp) i , etc. respectively. To estimate the directional derivative of θ at x k along p k , we divide it into three parts: D p k θ(x k)=H T(x k)BH(x k)p k=T 1+T 2+T 3,(3.5) where T 1=Σ i∈α k H i(BHp) i , T 2=Σ i∈β k H i(BHp) i , T 3=Σ i∈γ k H i(BHp) i . Consider i∈α k= k∪α -(x k) . In this case, we always have H i(BH(x)p) i=H i 2+H i(x i+p i) . If i∈ k , then H i(BHp) i -H i 2+|H i‖(T(x)p) i|. If i∈α -(x k) , then x i<0 . We have either x i+p i 0 , or x i+p i<0 . When x i+p i 0 , we get H i(BH(x)p) i -H i 2 .In the later case, x i+p i<0 , so H i(BH(x)p) i=-H i 2+|H i‖x i+p i|. Then, by elementary computation, we deduce that T 1 -Σi∈α kH i 2+Σ i∈α k|H i‖(T(x)p) i|.(3.6) Received March 1, 1995. 1991 MR Subject Classification: 05C25

Iterative Decoding of Parallel Concatenated Block Codes and Coset Based MAP Decoding Algorithm for F24 Code

A multi dimensional concatenation scheme for block codes is introduced, in which information symbols are interleaved and re encoded for more than once. It provides a convenient platform to design high performance codes with flexible interleaver size. Coset based MAP soft in/soft out decoding algorithms are presented for the F24 code. Simulation results show that the proposed coding scheme can achieve high coding gain with flexible interleaver length and very low decoding complexity.

Measures for Error Avalanche and Energy Avalanche Effect in Secure Wireless Fieldbus Systems

The wireless fieldbus is a vital part in present industrial automatic controls and software-defined systems. Accompanying, security is an upcoming problem determines its future leapfrog development. Wireless fieldbus systems can be made secure by encrypting the data. Unfortunately, the diffusion character of encryption brings significant vulnerabilities in terms of deteriorated error performance and energy efficiency. In this paper, we first propose an AES-dependent Hsiao(AD-Hsiao) code to improve the error correction capability, which leverages the prior information of data similarity and AES decryption to assist syndrome decoding. Then, we develop "Random Coset" scheme to reduce energy consumption. Based on mapping written data into several data candidates, this scheme lessens the number of bits written to memory and thereby boosts the write energy efficiency. Simulation results show that the AD-Hsiao code can correct majority of double errors in a single codeword with limited latency and area cost as the Hamming code. Moreover, the(72,64) AD-Hsiao code improves the reliability by 102 over the(72,64) Hamming code at 8 dB AWGN channel, and also exceeding the high cost(78,64) BCH code. In addition, the "Random Coset" improves energy efficiency by 6.6～14% than the current scheme while re-quires small ROM storage.

Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target withℤ2n Grading

The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target withℤ2n grading is derived using a first−order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints.This enables us to show that the conserved charges of the theory are in involution.When n=2,our results coincide with the results given by Magro for the pure spinor description of AdS5×S5 string theory(when the ghost terms are omitted).

ON THE DIMENSION AND MINIMUM DISTANCE OF BCH CODES OVER GF(q)

In this paper, only narrow-sense primitive BCH codes over GF(q) are considered. A formula, that can be used in many cases, is first presented for computing the dimension of BCH codes. It improves the result given by MacWilliams and Sloane in 1977. A new method for finding the dimension of all types of BCH codes is proposed. In second part, it is proved that the BCH bound is the leader of some cyclotomic coset, and we guess that the minimum distance for any BCH code is also the leader of some cyclotomic coset.

COSET PARTITION OF ADDITIVE GROUPS AND MINORITY-LOGIC DECODING ALGORITHM FOR RM CODES

Two new notions for the coset partition of dyadic additive groups are proposed,andtheir sufficient and necessary conditions are also given.On the basis of these works,the feasibilityproblem of implementing minority-logic decoding algorithm for RM codes is solved.

FINITE PERMUTATION REPRESENTATION OF A SUBGROUP OF PICARD GROUP

We investigate action of a subgroup G1 of the Picard group on finite sets using coset diagrams. We show that its actions on the sets of 3, 4, 5, 6, 8, and 12 elements yield building blocks of Coset diagrams and that these blocks can be connected together so that a diagram of n vertices can be obtained. We show that various combinations of these blocks represent alternating and symmetric groups of various degrees. We show also that the action of G1 on a set of n vertices is transitive.

COSET DIAGRAMS FOR A HOMOMORPHIC IMAGE OFΔ(3,3,k)

Let q be a prime power. By PL（Fq） the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △（3, 3, k） = （u, v： u^3 = v^3 = （uv）^k = 1〉on PL（Fq）, where q ≡ ±1（modk）. Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △（3, 3, k） on PL（Fq）. The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by （u^-v^-）^k. In this way, they get △（3, 3, k） as permutation groups on PL（Fq）.

Palm Vein Authentication Based on the Coset Decomposition Method

The palm vein authentication technology is extremely safe, accurate and reliable as it uses the vascular patterns contained within the body to confirm personal identification. The pattern of veins in the palm is complex and unique to each individual. Its non-contact function gives it a healthful advantage over other biometric technologies. This paper presents an algebraic method for personal authentication and identification using internal contactless palm vein images. We use MATLAB image processing toolbox to enhance the palm vein images and employ coset decomposition concept to store and identify the encoded palm vein feature vectors. Experimental evidence shows the validation and influence of the proposed approach.

On Inclusion of Permutation Modules

Let H1,H2 be subgroups of a finite group G. Assume that G = umlH2yiH1 = n Uj=1 HlgiH1 and that y1=1,g1= 1. Let Di be the set consisting of right cosets of H~ contained in H2yiH1 and let dj （j --- 1,..., n） be the set consisting of right cosets contained in HlgjH1. We define the n x m matrix Mz （z = 1,..., m） whose columns and rows are indexed by Di and dj respectively and the （dk, Dz） entry is ｜Dzgk N Dl]. Let M =（M1 , Mm）. Assume that 1GH1 and 1H2G are semisimple permutation modules of a finite group G. In this paper, by using the matrix M, we give some sufficient and necessary conditions such that 1~1 is isomorphic to a submodule of 1H2G. As an application, we prove Foulkes＇ conjecture in special cases.

New Quantum MDS Code from Constacyclic Codes

In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable(MDS for short) codes from constacyclic MDS codes through the Hermitian construction. In this paper, a new class of quantum MDS code is constructed, which extends the result of [Theorems 3.14–3.15, Kai, X., Zhu, S., and Li,P., IEEE Trans. on Inf. Theory, 60(4), 2014, 2080–2086], in the sense that our quantum MDS code has bigger minimum distance.

A result on certain coset subalgebras of the βγ-system

In this paper, for the highest weight module V4 of sl（2,C） with the highest weight 4, we describe subalgebras Sβ（V4）＋ and Sγ（V4）＋ of the βγ-system coset S（V4）＋ by giving their generators. These eoset subalgebras are interesting, new examples of strongly finitely generated vertex algebra.

Amalgams of Rank 2 and Characteristic 3 Involving M_(11)

In this paper we investigate the amalgams (M11,X) of rank 2 and characteristic 3,where X is a group of Lie type of rank 1 or permutation group of low rank,and give a characterization of the 3 local subgroups of the finite sporadic groups Co3 of Ly and Suz.

Notes on index of quantum integrability

A quantum integrability index was proposed in Komatsu et al(2019 SciPost Phys.7065).It systematizes the Goldschmidt and Witten's operator counting argument(Goldschmidt and Witten 1980 Phys.Lett.B 91392)by using the conformal symmetry.In this work we compute the quantum integrability indexes for the symmetric coset models SU(N)/SO(N)and SO(2N)/SO(N)×SO(N).The indexes of these theories are all non-positive except for the case of SO(4)/SO(2)×SO(2).Moreover we extend the analysis to the theories with fermions and consider a concrete theory:the CP~N model coupled with a massless Dirac fermion.We find that the indexes for this class of models are non-positive as well.

Heptavalent Symmetric Graphs with Certain Conditions

A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group G of automorphisms,then either G is normal in Aut(Γ),or Aut(Γ)contains a non-abelian simple normal subgroup T such that G≤T and(G,T)is explicitly given as one of 11 possible exceptional pairs of non-abelian simple groups.If G is arc-transitive,then G is always normal in Aut(Γ),and if G is regular on the vertices of Γ,then the number of possible exceptional pairs(G,T)is reduced to 5.

Arc-Transitive Graphs of Square-free Order with Valency 11

In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and the graphs associated with the simple group J1 and PSL(2,p),where p is a prime.

P-Condense and LP-Condensing Operatorson Semilattices,Join-Complete Lattices and Some Inverse Semigroups

In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices,and inversesemigroups.As an application of our results,we also show that the unary operations*:Hg→Hg-1 Hg and*:Hg→HG on the coset semigroupK(G)of a group G are-condensing operators.Consequently,a necessary and sufficient condition for theseoperators to be 69-condensing operators is given.Some further results on condensesemigroups considered by Chen et al.(Acta Math.Hung.119:281-305,2008)arediscussed and obtained in this paper.