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.

BILINEAR FORMS AND LINEAR CODES

Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.

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.

Optimal Asymmetric Quantum Codes from the Euclidean Sums of Linear Codes

In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.

New construction of highly nonlinear resilient S-boxes via linear codes

Highly nonlinear resilient functions play a crucial role in nonlinear combiners which are usual hardware oriented stream ciphers.During the past three decades,the main idea of construction of highly nonlinear resilient functions are benefited from concatenating a large number of affine subfunctions.However,these resilient functions as core component of ciphers usually suffered from the guess and determine attack or algebraic attack since the n-variable nonlinear Boolean functions can be easily given rise to partial linear relations by fixing at most nil variables of them.How to design highly nonlinear resilient functions(S-boxes)without concatenating a large number of nil variables affine subfunctions appears to be an important task.In this article,a new construction of highly nonlinear resilient functions is proposed.These functions consist of two classes subfunctions.More specially,the first class(nonlinear part)contains both the bent functions with 2k variables and some affine subfUnctions with n/2-k variables which are attained by using[n/2-k,m,d]disjoint linear codes.The second class(linear part)includes some linear subfunctions with nil variables which are attained by using[n/2,m,d]disjoint linear codes.It is illustrated that these resilient functions have high nonlinearity and high algebraic degree.In particular,It is different from previous well-known resilient S-boxes,these new S-boxes cannot be directly decomposed into some affine subftinctions with nil variables by fixing at most nil variables.It means that the S-boxes(vectorial Boolean functions)which use these resilient functions as component functions have more favourable cryptography properties against the guess and determine attack or algebraic attacks.

Weight hierarchies of linear codes satisfying the almost chain condition

The weight hierarchy of a linear [n, k;q] code C over GF(q) is the sequence (d1,d2,..., dk) where dr is the size of the smallest support of an r-dimensional subcode of C. An [n,k;q] code satisfies the chain condition if there exists subcodes D1 D2 … Dk = C of C such that Dr has dimension r and support of size dr for all r. Further, C satisfies the almost chain condition if it does not satisfy the chain condition, but there exist subcodes Dr of dimension r and support of size dr for all r such that D2 D3 Dk = C and D1 D3. A simple necessary condition for a sequence to be the weight hierarchy of a code satisfying the almost chain condition is given. Further, explicit constructions of such codes are given, showing that in almost all cases, the necessary conditions are also sufficient.

A Class of the Hamming Weight Hierarchy of Linear Codes with Dimension 5

The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new pre- conditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.

A Novel Secret Sharing Scheme Based on Minimal Linear Codes

In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we partition the underlying minimal linear code into disjoint classes, establishing a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. Each participant, with only one short share transmitted through a public channel, can share a large secret. Therefore, the proposed scheme can distribute a large secret in practical applications such as secure information dispersal in sensor networks and secure multiparty computation.

Optimal and suboptimal structured algorithms of binary linear block codes

The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matrix.Based upon the property of generator matrix,the structured algorithms of linear block codes are demonstrated.Since the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured algorithm.The comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths.Because the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.

Distinction of self-synchronous scrambled linear blockcodes based on multi-fractal spectrum

This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.

Linear Dispersion Orthogonal Space-Time Block Codes

A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC.The scheme proposed is named linear dispersion orthogonal space-time block codes （LDOSTBC）.In LDOSTBC scheme,firstly,the data is coded into LDC codewords.Then,the coded LDC substreams are coded into OSTBC codewords again.The decoding algorithm of LDOSTBC combines linear decoding of OSTBC and ML decoding or suboptimum detection algorithms of LDC.Compared with OSTBC scheme when the rate of LDC is MtR,the performance of LDOSTBC scheme can be improved without decreasing the data rate,where Mt is the number of transmit antennas and R is the spectral efficiency of the modulation constellation.If some rate penalty is allowed,when the rate of LDC is less than MtR the performance of LDOSTBC can be improved further.

On the Computing of the Minimum Distance of Linear Block Codes by Heuristic Methods

The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.

On Latency Reductions in Vehicle-to-Vehicle Networks by Random Linear Network Coding

In the Internet of vehicles(IoV),direct communication between vehicles,i.e.,vehicle-tovehicle(V2V)may have lower latency,compared to the schemes with help of Road Side Unit(RSU)or base station.In this paper,the scenario where the demands of a vehicle are satisfied by cooperative transmissions from those one in front is considered.Since the topology of the vehicle network is dynamic,random linear network coding is applied in such a multisource single-sink vehicle-to-vehicle network,where each vehicle is assumed to broadcast messages to others so that the intermediate vehicles between sources and sink can reduce the latency collaboratively.It is shown that the coding scheme can significantly reduce the time delay compared with the non-coding scheme even in the channels with high packet loss rate.In order to further optimize the coding scheme,one can increase the generation size,where the generation size means the number of raw data packets sent by the source node to the sink node in each round of communication.Under the premise of satisfying the coding validity,we can dynamically select the Galois field size according to the number of intermediate nodes.It is not surprised that the reduction in the Galois field size can further reduce the transmission latency.

NEW SECRET SHARING SCHEME BASED ON LINEAR CODE

A secret sharing system can be damaged when the dealer cheating occurs.In this paper,two kinds of secret sharing schemes based on linear code are proposed.One is a verifiable scheme which each participant can verify his own share from dealer's distribution and ensure each participant to receive valid share.Another does not have a trusted center,here,each participant plays a dual-role as the dealer and shadow(or share) provider in the whole scheme.

THE AUTOMORPHISM GROUP OF A LINEAR CODE

We know that for a code C,it‘s very important to find out the Automorphism groupAutC of C.However,it is very difficult to seek entire AutC.In this paper,using the G.I of matrices over a finite field,we give several methods to judge whether a permutation σ∈S_n.(Symmetric group) belongs to AutC or not.They are helpful for the purpose to ex-

A New Description of the Additive Quantum Codes

A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several consequences and examples of good quantum codes by using our new description of the additive quantum codes.

HY-PC:Enabling Consistent Positioning and Communication Using Visible Light

Visible light(VL)plays an important role in achieving high-precision positioning and low bit error radio(BER)data communication.However,most VL-based systems can not achieve positioning and communication,simultaneously.There are two problems:1)the hybrid systems are difficult to extract distinguishable positioning beacon features without affecting communication performance,2)in the hybrid systems,the lost data bits in the inter-frame gap(IFG)are hard to recover,which affects positioning and communication performance.Therefore,in this article,we propose a novel VL-based hybrid positioning and communication system,named HY-PC system,to solve the above problems.First,we propose the robust T-W mapping for recognizing specific Light Emitting Diodes(LEDs),which can provide stable LED recognition accuracy without adding extra beacon data and does not decrease the communication rate.Furthermore,we also propose the novel linear block coding and bit interleaving mechanism,which can recover the lost data bits in the IFG and improve data communication performance.Finally,we use commercial off-the-shelf devices to implement our HY-PC system,extensive experimental results show that our HY-PC system can achieve consistent high-precision positioning and low-BER data communication,simultaneously.

Gray Images of Constacyclic Codes over a Non-chain Extension of Z_(4)

Let Z_(4) be the ring of integers modulo 4.We study the Λ-constacyclic and(θ,Λ)-cyclic codes over the non-chain ring R=Z_(4)[u,v]/<u^(2)=1,v^(2)=0,uv=vu=0>for a unit Λ=1+2u+2v in R.We define several Gray maps and find that the respective Gray images of a quasi-cyclic code over Z_(4) are cyclic,quasi-cyclic or permutation equivalent to this code.For an odd positive integer n,we determine the generator polynomials of cyclic and Λ-constacyclic codes of length n over R.Further,we prove that a(θ,Λ)-cyclic code of length n is a Λ-constacyclic code if n is odd,and a Λ-quasi-twisted code if n is even.A few examples are also incorporated,in which two parameters are new and one is best known to date.

Cyclic Co des over F2＋uF2＋v F2

We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cyclic code length 3n over F2.

Robust Speech Recognition System Using Conventional and Hybrid Features of MFCC,LPCC,PLP,RASTA-PLP and Hidden Markov Model Classifier in Noisy Conditions

In recent years, the accuracy of speech recognition (SR) has been one of the most active areas of research. Despite that SR systems are working reasonably well in quiet conditions, they still suffer severe performance degradation in noisy conditions or distorted channels. It is necessary to search for more robust feature extraction methods to gain better performance in adverse conditions. This paper investigates the performance of conventional and new hybrid speech feature extraction algorithms of Mel Frequency Cepstrum Coefficient (MFCC), Linear Prediction Coding Coefficient (LPCC), perceptual linear production (PLP), and RASTA-PLP in noisy conditions through using multivariate Hidden Markov Model (HMM) classifier. The behavior of the proposal system is evaluated using TIDIGIT human voice dataset corpora, recorded from 208 different adult speakers in both training and testing process. The theoretical basis for speech processing and classifier procedures were presented, and the recognition results were obtained based on word recognition rate.