Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let C(t,e) denote the cyclic code with two nonzero αt and αe, where α is a generator of 𝔽*3m. In this letter, we investigate the ternary cyclic codes with parameters [3m - 1, 3m - 1 - 2m, 4] based on some results proposed by Ding and Helleseth in 2013. Two new classes of optimal ternary cyclic codes C(t,e) are presented by choosing the proper t and e and determining the solutions of certain equations over 𝔽3m.

The calculation of cross-correlation between a sequence with good autocorrelation and its decimated sequence is an interesting problem in the field of sequence design. In this letter, we consider a class of ternary sequences with perfect autocorrelation, proposed by Shedd and Sarwate (IEEE Trans. Inf. Theory, 1979, DOI: 10.1109/TIT.1979.1055998), which is generated based on the cross-correlation between m-sequence and its d-decimation sequence. We calculate the cross-correlation distribution between a certain pair of such ternary perfect sequences and show that the cross-correlation takes three different values.

A unified construction for yielding optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences was proposed by Zeng et al. In this paper, the linear complexity over finite field 𝔽2, 𝔽4 and Galois ring ℤ4 of the quaternary sequences are discussed, respectively. The exact values of linear complexity of sequences obtained by Legendre sequence pair, twin-prime sequence pair and Hall's sextic sequence pair are derived.

Binary bent functions have a strictly specified number of non-zero values. In the same way, ternary bent functions satisfy certain requirements on the elements of their value vectors. These requirements can be used to specify six classes of ternary bent functions. Classes are mutually related by encoding of function values. Given a basic ternary bent function, other functions in the same class can be constructed by permutation matrices having a block structure similar to that of the factor matrices appearing in the Good-Thomas decomposition of Cooley-Tukey Fast Fourier transform and related algorithms.

Let G11 (resp., G12) be the ternary Golay code of length 11 (resp., 12). In this letter, we investigate the separating redundancies of G11 and G12. In particular, we determine the values of sl(G11) for l = 1, 3, 4 and sl(G12) for l = 1, 4, 5, where sl(G11) (resp., sl(G12)) is the l-th separating redundancy of G11 (resp., G12). We also provide lower and upper bounds on s2(G11), s2(G12), and s3(G12).

Sequences that attain the smallest possible absolute sidelobes (SPASs) of periodic autocorrelation function (PACF) play fairly important roles in synchronization of communication systems, Large scale integrated circuit testing, and so on. This letter presents an approach to construct 16-QAM sequences of even periods, based on the known quaternary sequences. A relationship between the PACFs of 16-QAM and quaternary sequences is established, by which when quaternary sequences that attain the SPASs of PACF are employed, the proposed 16-QAM sequences have good PACF.

This letter presents ternary convolutional codes and their punctured codes with optimum distance spectrum.

The present paper introduces a novel type of structured ternary sequences having a zero-correlation zone (zcz) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation function of the proposed sequence set are zero for phase shifts within the zcz. The proposed zcz sequence set can be generated from an arbitrary pair of an Hadamard matrix of order lh and a binary/ternary perfect sequence of length lp. The sequence set of order 0 is identical to the r-th row of the Hadamard matrix. For m ≥ 0, the sequence set of order (m+1) is constructed from the sequence set of order m by sequence concatenation and interleaving. The sequence set has lp subsets of size 2lh. The periodic correlation function and the aperiodic correlation function of the proposed sequence set have a zcz from -(2m+1-1) to 2m+1-1. The periodic correlation function and the aperiodic correlation function of the sequences of the i-th subset and k-th subset have a zcz from -2m+2-(lh+1)((j-k) mod lp) to -2m+2-(lh+1)((j-k) mod lp). The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth-generation mobile networks.

In this letter, two new families of quaternary sequences with low four-level or five-level autocorrelation are constructed based on generalized cyclotomy over Z2p. These quaternary sequences are balanced and the maximal absolute value of the out-of-phase autocorrelation is 4.

A family of quaternary sequences over Z4 is defined based on the Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd primes p and q. The linear complexity is determined by computing the defining polynomial of the sequences, which is in fact connected with the discrete Fourier transform of the sequences. The results show that the sequences possess large linear complexity and are “good” sequences from the viewpoint of cryptography.

The conventional generalized spatial modulation (GSM) simultaneously activates multiple transmit antennas in order to improve the spectral efficiency of the original SM. In this letter, to lessen the hardware burden of the multiple RF chains, we provide a new scheme that is designed by combining the GSM scheme using only two active antennas with quaternary quasi-orthogonal sequences of a length of two. Compared with the other SM schemes, the proposed scheme has significant benefits in average error performances and/or their hardware complexities of the RF systems.

Locally repairable code (LRC) can recover any codeword symbol failure by accessing a small number of other symbols, which can increase the efficiency during the repair process. In a distributed storage system with locally repairable codes, any node failure can be rebuilt by accessing other fixed nodes. It is a promising prospect for the application of LRC. In this paper, some methods of constructing matrices which can generate codes with small locality will be proposed firstly. By analyzing the parameters, we construct the generator matrices of the best-known ternary linear codes of dimension 6, using methods such as shortening, puncturing and expansion. After analyzing the linear dependence of the column vectors in the generator matrices above, we find out the locality of the codes they generate. Many codes with small locality have been found.

The present paper introduces a novel construction of structured ternary sequences having a zero-correlation zone (ZCZ) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation function of the proposed sequence set are zero for phase shifts within the ZCZ. The proposed ZCZ sequence set can be generated from an arbitrary Hadamard matrix of order n. The sequence set of order 0 is identical to the r-th row of the Hadamard matrix. For m≥0, the sequence set of order (m+1) is constructed from the sequence set of order m by sequence concatenation and interleaving. The sequence set of order m has 2m subsets of size n. The length of the sequence is equal to n4m+2m+1(2m-1); The phase shift of the ZCZ for the whole sequence set is from -(2m-1) to (2m-1). The sequence set of order 0 is coincident with the rows of the given Hadamard sequence with no ZCZ. The subsets can be associated with a perfect binary tree of height m with 2m leaves. The r-th sequence subset consists of from the nr-th sequence to the ((n+1)r-1)-th sequence. The r-th subset is assigned to the r-th leaf of the perfect binary tree. For a longer distance between the corresponding leaves to the r-th and s-th sequences, the ZCZ of the r-th and s-th sequences is wider. This tree-structured width of ZCZ of a pair of the proposed sequences enables flexible design in applications of the proposed sequence set. The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth generation of radio access networks.

Ternary content addressable memory (TCAM), which can store 0, 1, or X in its cells, is widely used to store routing tables in network routers. Negative bias temperature instability (NBTI) and positive bias temperature instability (PBTI), which increase Vth and degrade transistor switching speed, have become major reliability challenges. This study analyzes the signal probability of routing tables. The results show that many cells retain static stress and suffer significant degradation caused by NBTI and PBTI effects. The bit flipping technique is improved and proactive power gating recovery is proposed to mitigate NBTI and PBTI effects. In order to maintain the functionality of TCAM after bit flipping, a novel TCAM cell design is proposed. Simulation results show that compared to the original architecture, the bit flipping technique improves read static noise margin (SNM) for data and mask cells by 16.84% and 29.94%, respectively, and reduces search time degradation by 12.95%. The power gating technique improves read SNM for data and mask cells by 12.31% and 20.92%, respectively, and reduces search time degradation by 17.57%. When both techniques are used, read SNM for data and mask cells is improved by 17.74% and 30.53%, respectively, and search time degradation is reduced by 21.01%.

In this correspondence, a method of constructing optimal zero correlation zone (ZCZ) sequence sets over the 16-QAM+ constellation is presented. Based on 16-QAM orthogonal matrices and perfect ternary sequences, 16-QAM+ ZCZ sequence sets are obtained. The resulting ZCZ sequence sets are optimal with respect to the Tang-Fan-Matsufuji bound. Moreover, methods for transforming binary or quaternary orthogonal matrices into 16-QAM orthogonal matrices are proposed. The proposed 16-QAM+ ZCZ sequence sets can be potentially applied to communication systems using a 16-QAM constellation to remove the multiple access interference (MAI) and multi-path interference (MPI).

In this paper, we derive two simple asymptotic closed-form formulas for the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with Gray encoding and a simple asymptotic approximation for the average symbol error probability (SEP) of doubly-differential quaternary phase shift keying (DDQPSK) in Nakagami-m fading channels. Compared with the existing BEP/SEP expressions, the derived concise formulas are much more effective in evaluating the asymptotic properties of DQPSK/DDQPSK with various Nakagami fading parameters, the accuracy of which is verified by extensive numerical results.

In this letter, a local pattern coding scheme is proposed to reduce the dimensionality of feature vectors in the local ternary pattern. The proposed method encodes the ternary patterns into a binary pattern by clustering similar ternary patterns. The experimental results show that the proposed method outperforms the previous methods.

Let r be an odd prime, such that r≥5 and r≠p, m be the order of r modulo p. Then, there exists a 2pth root of unity in the extension field Frm. Let G(x) be the generating polynomial of the considered quaternary sequences over Fq[x] with q=rm. By explicitly computing the number of zeros of the generating polynomial G(x) over Frm, we can determine the degree of the minimal polynomial, of the quaternary sequences which in turn represents the linear complexity. In this paper, we show that the minimal value of the linear complexity is equal to $ rac{1}{2}(3p-1) $ which is more than p, the half of the period 2p. According to Berlekamp-Massey algorithm, these sequences viewed as enough good for the use in cryptography.

Perfect arrays are widely applied to high-dimensional communications, time-frequency-coding, spatial correlation or map matching, built-in tests of VLSI-circuits, radar, and so on. The letter investigates perfect arrays over the 8-QAM+ constellation, and two constructions for yielding such arrays are presented. Furthermore, the family size of the proposed arrays is determined as well.

In this letter, we give a trace representation of binary Jacobi sequences with period pq over an extension field of the odd prime field Fr. Our method is based on the use of a pqth root of unity over the extension field, and the representation of the Jacobi sequences by corresponding indicator functions and quadratic characters of two primes p and q.