Linear Codes with Two Weights or Three Weights from Two Types of Quadratic forms

Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.

A Note on m-Weights of Linear Codes

m-weight, as a new generalization of classical Hamming weight, was discussedin this paper. A condition for the existence of linear codes of certain m-weights was given; theSingleton bound, Plotkin bound and Sphere Parking bound of Hamming weight were correspondinglygeneralized to the m-weight.

Study on cipher propertys of constant weight codes

Constant weight code is an important error-correcting control code in communications. Basic structure of constant weight codes for some arriving at Johnson bound, A（n, 2u, w）, is presented. Some correlative propertys of the codes, the solution of arriving at Johnson bound, and the results on the couple constant code and some constant weight codes are discussed. The conclusion is verified through four examples.

On the complete weight distributions of quantum error-correcting codes

In a recent paper, Hu et al. defined the complete weight distributions of quantum codes and proved the Mac Williams identities, and as applications they showed how such weight distributions may be used to obtain the singleton-type and hamming-type bounds for asymmetric quantum codes. In this paper we extend their study much further and obtain several new results concerning the complete weight distributions of quantum codes and applications. In particular, we provide a new proof of the Mac Williams identities of the complete weight distributions of quantum codes. We obtain new information about the weight distributions of quantum MDS codes and the double weight distribution of asymmetric quantum MDS codes. We get new identities involving the complete weight distributions of two different quantum codes. We estimate the complete weight distributions of quantum codes under special conditions and show that quantum BCH codes by the Hermitian construction from primitive, narrow-sense BCH codes satisfy these conditions and hence these estimate applies.

Construction and Weight Distributions of Binary Linear Codes Based on Deep Holes

Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.

Hybrid weighted symbol-flipping decoding for nonbinary LDPC codes

A hybrid decoding algorithm is proposed for nonbinary low-density parity-check （LDPC） codes, which combines the weighted symbol-flipping （WSF） algorithm with the fast Fourier trans- form q-ary sum-product algorithm （FFT-QSPA）. The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low- eomplexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. Simulation results show that the proposed hybrid algorithm greatly reduces the computational complexity with the performance close to that of FFT-QSPA.

Lexicographic Constant-Weight Equidistant Codes over the Alphabet of Three, Four and Five Elements

In this paper we consider the problem of finding bounds on the size of lexicographic constant-weight equidistant codes over the alphabet of three, four and five elements with 2 ≤ w 【n ≤ 10. Computer search of lexicographic constant-weight equidistant codes is performed. Tables with bounds on the size of lexicographic constant-weight equidistant codes are presented.

Theoretical Analysis of Bit-Error Probability for Convolutional Codes with Weight Enumerators

The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function)T[x,y] of convolutional codes.Next use computer simulation to compare upper bound on the bit error probability on an additive white Gaussian noise(AWGN) for maximum free distance(MFD) codes of previously found and optimum distance spectrum(ODS) codes with rate 1/4,overall constraint length are 5 and 7,respectively.Finally,a method of how to search for good convolutional codes is given.

Error Probability for Convolutional Codes with Weight Enumerating Function

The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function) T[x,y] of convolutional codes.Next use computer simulation to compare upper bound on the bit error probability on an additive white Gaussian noise (AWGN) for maximum free distance (MFD) codes of previously found and optimum distance spectrum (ODS) codes with rate 1/4,overall constraint length are 5 and 7,respectively. Finally,a method of how to search for good convolutional codes is given.

Malicious Code Modeling and Analysis in Weighted Scale-Free Networks

We study the detailed malicious code propagating process in scale-free networks with link weights that denotes traffic between two nodes. It is found that the propagating velocity reaches a peak rapidly then decays in a power-law form, which is different from the well-known result in unweighted network case. Simulation results show that the nodes with larger strength are preferential to be infected, but the hierarchical dynamics are not clearly found. The simulation results also show that larger dispersion of weight of networks leads to slower propagating, which indicates that malicious code propagates more quickly in unweighted scale-free networks than in weighted scale-free networks under the same condition. These results show that not only the topology of networks but also the link weights affect the malicious propagating process.

Combinatorial design-based quasi-cyclic LDPC codes with girth eight

This paper presents a novel regular Quasi-Cyclic (QC)Low Density Parity Check (LDPC)codes with columnweight three and girth at least eight.These are designed on the basis of combinatorial design in which subsets applied for the construction of circulant matrices are determined by a particular subset.Considering the nonexistence of cycles four and six in the structure of the parity check matrix,a bound for their minimum weight is proposed.The simtdations conducted confirm that without applying a masking technique,the newly implemented codes have a performance similar to or better than other well-known codes.This is evident in the waterfall region, while their error floor at very low Bit Error Rate (BER)is expected.

GAUSS PERIODS AND CYCLIC CODES FROM CYCLOTOMIC SEQUENCES OF SMALL ORDERS

Let p =ef +1 be an odd prime with positive integers e and f. In this paper, we calculate the values of Gauss periods of order e =3, 4, 6 over a finite field GF(q), where q is a prime with q≠p. As applications, several cyclotomic sequences of order e =3, 4, 6 are employed to construct a number of classes of cyclic codes over GF(q) with prime length. Under certain conditions, the linear complexity and reciprocal minimal polynomials of cyclotomic sequences are calculated, and the lower bounds on the minimum distances of these cyclic codes are obtained.

Turbo Codes with Modified Code-matched Interleaver over A WGN and Rayleigh Fading Channel

A novel Code-Matched interleaver is proposed which decreases the number of the low weight codewords to improve the performance of the Turbo code. The modified design can adapt more kinds of Turbo codes determined by the generator matrix, while it doesn＇t decrease the bit error rate performance of Turbo codes at moderate to high signal to noise ratio. At the same time, in Rayleigh fading channel, the new Code-Matched interleaver can also debase the error floor.

Two Classes of Quaternary Codes from Z_4-valued Quadratic Forms

Let R=GR (4,m)be a Galois ring with Teichmuller set T_m and Tr_m be the trace function fromRto Z_4.In this paper,two classes of quaternary codes C_1 = {c(a,b):a ∈R,b ∈ T_(m/2)},where c(a,b)=(Tr_m(ax)+Tr_(m/2)(2 bx^(2 m/2 +1)))_(x∈T_m),and C_2= {c(a,b):a ∈ R,b ∈ T_m}, where c(a,b)=(Tr_m(ax+2 bx^(2 k+1)))_(x∈T_m),and m/gcd(m,k)is even,are investigated,respectively.The Lee weight distributions,Hamming weight distributions and complete weight distributions of the codes are completely given.

A Weight-Coded Evolutionary Algorithm for the Multidimensional Knapsack Problem

A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm pro-posed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.

Linear Codes over the Finite Ring <i>Z</i>₁₅

In this paper, the structure of the non-chain ring Z15 is studied. The ideals of the ring Z15 are obtained through its non-units and the Lee weights of elements in Z15 are presented. On this basis, by the Chinese Remainder Theorem, we construct a unique expression of an element in Z15. Further, the Gray mapping from Zn15 to Z2n15 is defined and it’s shown to be distance preserved. The relationship between the minimum Lee weight and the minimum Hamming weight of the linear code over the ring Z15 is also obtained and we prove that the Gray map of the linear code over the ring Z15 is also linear.

Several Classes of Two-weight or Three-weight Linear Codes and Their Applications

Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].

改进型Code-Matched交织器

Turbo码作为信道编码方案 ,可以获得较高的误比特率 (BER)性能 ,而交织器的设计是影响Turbo码性能的关键环节 .笔者在码的重量分析的基础上提出了一种改进型Code Matched交织器 ,它可以减少低重量码的数量 ,从而提高Turbo码的性能 .这种改进型Code Matched交织器可以适用于多种不同生成矩阵产生的Turbo码 ,而且不会影响Turbo码在中、高信噪比处的性能 ,同时 ,在Rayleigh信道下 。

Kravchenko probabilityweight functions in problems of radar signals correlation processing

In this report the combined method of correlation radar signal(RS)processing based on the theory of atomic functions(AF)is examined.Examples of using of new Kravchenko probability weight functions(WF)designs are presented.Quality functional to estimate accuracy and efficiency of RS processing for concrete physical models is constructed.It is shown that the proposed approach significantly improves the quality of the coherent analysis of RS.

The Digital Fingerprinting Method for Static Images Based on Weighted Hamming Metric and on Weighted Container Model

The algorithm of fingerprint constructing for still images based on weighted image structure model is proposed. The error correcting codes that are perfect in weighted Hamming metric are used as a base for fingerprint constructing.