The undetected error probabilities of combinatorial codes and their dual codes

IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byPe（p） = sum from i=1 Aipi（1-p）n-1, （1）where （A0, A1,…, An） is the weight distribution of C. If for all 0≤p≤0.5, Pe（p）≤Pe（0. 5） = 2k-n-2-n, then C is called good for error detection. Moreover, if Pe （p） ismonotonously increasing in the interval [0, 0.5], then C is called proper. Clearly, propercodes are good.

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.

CONSTACYCLIC CODES OF ARBITRARY LENGTHS OVER RING Z_(p^m) +vZ_(p^m)

By constructing a Gray map, constacyclic codes of arbitrary lengths over ring R =Z p m +vZ pmare studied, wherev 2=v. The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular,(1 +(v +1)ap)-constacyclic codes over R are classified in terms of generator polynomial, where a is a unit of Z m.

PERIOD DISTRIBUTION OF CYCLIC CODES OVER F_q + uF_q +···+u^(m-1)F_q

In this paper, the period distribution of cyclic codes overR = F_q + uF_q +···+u^(m-1)F_q is studied, where um= 0 and q is a prime power. A necessary and sufficient condition for the existence of period of cyclic codes over R is given. The period distributions of cyclic codes over R and their dual codes are determined by employing generator polynomial. The counting formulas of the period distributions of cyclic codes over R and their dual codes are obtained.

SKEW CYCLIC CODES OVER RING F_p+vF_p

In this paper, we study skew cyclic codes over the ring Fp +vFp,where p is a odd prime and v 2=1. We give the generators of skew cyclic codes, with the consideration of the dual of skew cyclic codes.

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.

Maximal codes

In this work we try to introduce the concept of Maximal codes that are built over rings, more precisely we will give Maximal codes for special rings, Namely that the notion of maximal codes has been used by Chritophe Chapote, these maximal codes are constructed over finite fields, and these codes are used for coding and decoding.

Beam shaping with limited amplitude weight values for satellite active phased array antenna

To gain the tradeoff between lower sidelobe and higher power amplifiers efficiency,a transmitting beam shaping scheme with limited amplitude weight values for satellite active phased array antenna is presented. The scheme is implemented by a dual coding genetic algorithm(GA). Phase and amplitude of array weight vectors for beam shaping are encoded by real coding and finite length binary coding,respectively,which,maintaining accuracy of results,reduces the amplitude dynamic range and improves the efficiency of power amplifiers. The presented algorithm,compared with complex-coded GA,increases the convergence rate due to the search space's decrease. In order to overcome the prematurity and obtain better global optimization or quasi-global optimization,a new dual coding GA based on "species diversity retention" strategy and adaptive crossover and mutation probability are presented.

A Novel High Spectral Efficiency Waveform Coding-OVFDM

Based on the Overlapped Multiplexing Principle[12],a frequency domain OVFDM(Overlapped Frequency Domain Multiplexing) Coding is proposed.By the data weighted shift overlapped version of any band-limited Multiplexing Transfer Function H(f) the coding gain and spectral efficiency are both achieved.The heavier the overlap of the data weighted Multiplexing Transfer Function H(f),the higher the coding gain and spectral efficiency as well as the closer the output to the optimum complex Gaussian distribution.The bit error probability performance is estimated.The time domain OVTDM(Overlapped Time Domain Multiplexing) Coding,the dual of OVFDM in time domain is incidentally proposed as well.Both theoretical analysis and testified simulations show that OVFDM(OVTDM) is suitable for high spectral efficiency application and its spectral efficiency is only roughly linear to SNR rather than the well-known logarithm to SNR.

Tentative model of integrating authentic captioned video to facilitate ESL learning

Guided by relevant learning theories and based on the analysis of the attributes of captioned video, the Chinese ESL learners＇ characteristics and the characteristics of ESL learning itself, the paper tries to propose a model of integrating captioned video in ESL acquisition process. The model focuses on the feasibility of using captioned video to facilitate or support ESL learning.

Trade-off Optimization for Scalable Video Coding Streaming in Relay-Based OFDMA Networks

To achieve an optimal trade-off between video quality and energy efficiency in the uplink streaming of multi-user Scalable Video Coding (SVC) videos in relay-based Orthogonal Frequency Division Multiple Access (OFDMA) cellular networks, a cross-layer design framework that jointly selects the Transmission Policy (TP) for SVC video frames, assigns OFDMA subcarriers, and allocates power for each subcarrier is proposed. We apply the dual decomposition method to the problem, and obtain a TP selection subproblem for each SVC video adaptation and a resource allocation subproblem of Joint Subcarrier, Relay and Power Allocation (JSRPA). A second level of dual decomposition is used to divide the JSRPA problem into independent subcarrier subproblems. The proposed Crosslayer Trade-off Optimization (CTO) algorithm is sub-distributed with significantly low complexity. A performance evaluation with typical SVC video traces demonstrates that the proposed algorithm is able to converge and efficiently achieve the optimal trade-off between the video quality and energy consumption at the MSs for uplink SVC streaming.

Macwilliams Identities of Linear Codes over the Ring F_2+ uF_2+ vF_2

The Lee weight enumerators and the complete weight enumerators for the linear codes over ring R = F2 ＋ u F2 ＋ v F2 are defined and Gray map from R^nto F2^3n is constructed. By proving the fact that the Gray images of the self-dual codes over R are the self-dual codes over F2, and based on the Mac Williams identities for the Hamming weight enumerators of linear codes over F2, the Mac Williams identities for Lee weight enumerators of linear codes over R are given. Further, by introducing a special variable t, the Mac Williams identities for the complete weight enumerators of linear codes over R are obtained. Finally, an example which illustrates the correctness and function of the two Mac Williams identities is provided.

A Note on Skew Cyclic Codes over a Class of Rings

We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R.Moreover,we discuss possible extension of our results in the more general setting ofδR-dual skew constacyclic codes over R,whereδR is an automorphism of R.

A Class of Constacyclic Codes over Ring R+vR

By constructing a Gray map, a class of constacyclic codes over ring R = R＋ vR is studied. Using cyclic codes and negacyclic codes of length p^s over ring R, the structure of （1 - 2v）-constacyclic codes and dual codes of length p^s over ring R are given, the Gray images of （1 - 2v）-constacyclic codes in a particular case are also studied. It is shown that linear codes of length pS over ring R are （1 -2v）-constacyclic codes if and only if their Gray images are distance-invariant cyclic codes of length 2p^s over ring R.

Effects of age on live streaming viewer engagement:a dual coding perspective

Though the emerging live streaming industry has attracted growing attention,the dominant yanzhi category where streamers mostly interact with the audience through amateur talent shows and casual chats has not been widely investigated.To decode the mechanism behind the popularity of yanzhi streamers,this study draws on Dual Coding Theory(DCT)to posit that age estimated from a streamer’s face and voice can influence the level of viewer engagement.To validate our hypothesized relationships,274 one-minute video records ahead of a viewer commenting or/and gifting were collected and analyzed via deep learning algorithms.Analytical results attest to the negative effects of both facial and vocal age on viewer engagement,while their interaction has a positive impact on viewer engagement.

Construction of Repeated-Root Constacyclic Code of Length 8p^s over F_(p^m)

For any odd prime p, a classification of all cyclic and negacyclic codes of length 8ps over Fpm are obtained, which establishes the algebra structures in term of specified polynomial generators of such codes. Among other results, all self-dual negacyclic codes of length 8ps are obtained, and the structures of α-constacyclic and β-constacyclic codes of length 8ps over Fpm are established.