In this paper, the covert performance of the simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided Terahertz (THz) communication systems with rate-splitting multiple access (RSMA) over the generalized α-μ fading channel is studied, where the discrete phase error and noise power uncertainty are considered. By means of the Gaussian approximation and Gamma distribution, the closed-form outage probability (OP) of the legitimate users is firstly derived. Then, the covert performance of the system is analyzed, and average detection error probability (ADEP) is deduced for the warden, and resultant closed-form ADEP is obtained. By minimizing the ADEP, the optimal detection threshold is derived with closed-form expression. With these results, subject to the constraints of covertness and reliability, the power allocation (PA) coefficients are optimized to minimize the OP of the covert user. Two adaptive PA schemes based on two-dimensional (2D) and one-dimensional (1D) search methods are respectively proposed to achieve the solutions, and resulting lower OP is attained. Simulation results indicate that the theoretical OP and ADEP can agree the corresponding simulations well, and randomizing the noise power of warden can improve the covert performance. Moreover, the warden with the optimized threshold can obtain lower ADEP than that with a fixed threshold, and the system with two PA schemes has a lower OP than that with a fixed PA, especially the scheme based on 1D search has lower complexity while maintaining the superior performance.

Terahertz (THz) communication has received much attention recently for its large bandwidth availability, high data-rate transmission and alleviating the spectrum shortage, and it can meet the requirements of Internet of Things with large system capacity and networking capability. In this paper, the performance of multi-antenna THz communication systems with rate-splitting multiple access (RSMA) under the hardware impairments and imperfect successive interference cancelation (SIC) are investigated, where the THz channel is modeled as a composite fading channel including the molecular absorption effects, misalignment fading and small-scale α-μ fading. Taking the hardware impairments and imperfect SIC into account, the probability density function and cumulative distribution function of the effective channel gain are derived. A joint zero-forcing and maximum ratio transmission beamforming design is employed to eliminate the interference among devices. Then, with the performance analysis, the closed-form outage probability (OP) and diversity gain of the system are respectively deduced. By minimizing the OP, a closed-form power allocation (PA) scheme is proposed to adjust the PA coefficients between the common stream and private streams, and resultant lower OP is attained. Moreover, the closed-form expression of the ergodic sum rate (ESR) is derived by means of Fox-H function and the Meijer-G function. With this ESR expression, the asymptotic ESR at high signal to noise ratio (SNR) is also provided to gain further insights. Furthermore, a simple upper bound of the ESR is derived for performance evaluation based on the Jensen’s inequality. Simulation results show that the theoretical analysis is effective, and the proposed PA scheme can obtain lower OP. Besides, the impact of different system and fading parameters on the performance are also analyzed.

An [n, k, d] linear code is said to be maximum distance separable (MDS) or almost maximum distance separable (AMDS) ifd = n−k+1 ord=n−k, respectively. If a code and its dual code are both AMDS, then the code is said to be near maximum distance separable (NMDS). Fork= 3 andk= 4, there are many constructions of NMDS codes by adding some suitable projective points to arcs in PG(k− 1,q). In this paper, we consider the monomial equivalence problem for some NMDS codes with the same weight distributions and present new constructions of NMDS codes.

In this paper, we try to apply methods from topological data analysis (TDA) to study geometric properties invariant under code equivalence transformation, especially for the linear codes associated with almost perfect nonlinear (APN) functions which offer optimal resistance to differential attacks and are very important in the design of block ciphers in cryptography. By employing persistent homology from TDA and tools from graph theory, we present new CCZ-invariants for APN functions. Some of them are computationally efficient and sufficient to distinguish many known APN functions, includingx3andx9(resp.x33) over F27(resp. F29) for which previously known invariants fail to do so.

It is conjectured by Golomb and Welch around half a century ago that there is no perfect Lee codes$C$of packing radius$r$in$\mathbb {Z}^{n}$for$r\geq 2$and$n\geq 3$. In 2020, Leung and Zhou proved this conjecture for linear Lee codes with$r=2$. A natural question is whether it is possible to classify the second best, i.e., almost perfect linear Lee codes of packing radius 2. Partial results was obtained recently by Xu and Zhou. In this paper, we show that if such codes exist in$\mathbb {Z}^{n}$, then$n$must belong to$\{1,2, 11, 29, 47, 56, 67, 79, 104, 121, 134, 191\}$.

More than 50 years ago, Golomb and Welch conjectured that there is no perfect Lee codes$C$of packing radius$r$in$\mathbb {Z}^{n}$for$r\geq 2$and$n\geq 3$. Recently, Leung and the second author proved that if$C$is linear, then the Golomb-Welch conjecture is valid for$r=2$and$n\geq 3$. In this paper, we consider the classification of linear Lee codes with the second-best possibility, that is the density of the lattice packing of$ \mathbb Z^{n}$by Lee spheres$S(n,r)$equals$\frac {|S(n,r)|}{|S(n,r)|+1}$. We show that, for$r=2$and$n\equiv 0,3,4 \pmod {6}$, this packing density can never be achieved.

In this paper, we present two new families of APN functions. The first family is in bivariate form$\big (x^{3}+xy^{2}+ y^{3}+xy, x^{5}+x^{4}y+y^{5}+xy+x^{2}y^{2} \big)\,\,\vphantom {_{\int _{\int }}}$over${\mathbb F}_{2^{m}}^{2}$. It is obtained by adding certain terms of the form$\sum _{i}(a_{i}x^{2^{i}}y^{2^{i}},b_{i}x^{2^{i}}y^{2^{i}})$to a family of APN functions recently proposed by Gölo&gcaron;lu. The$\vphantom {_{\int _{\int }}}$second family has the form$L(z)^{2^{m}+1}+vz^{2^{m}+1}$over${\mathbb F}_{{2^{3m}}}$, which generalizes a family of APN functions by Bracken et al. from 2011. By calculating the$\Gamma $-rank of the constructed APN functions over${\mathbb F}_{2^{8}}$and${\mathbb F}_{2^{9}}$, we demonstrate that the two families are CCZ-inequivalent to all known families. In addition, the two new families cover two known sporadic APN instances over${\mathbb F}_{2^{8}}$and${\mathbb F}_{2^{9}}$, which were found by Edel and Pott in 2009 and by Beierle and Leander in 2021, respectively.

In this paper, we present a new family of maximum rank-distance (MRD) codes in$\mathbb F_{q}^{2n\times 2n}$of minimum distance$2\leq d\leq 2n$. In particular, when$d=2n$, we can show that the corresponding semifield is exactly a Hughes–Kleinfeld semifield. The middle and right nuclei of these MRD codes are both equal to$\mathbb F_{q^{n}}$. We also prove that the MRD codes of minimum distance$2< d< 2n$in this family are inequivalent to all known ones. The equivalence between any two members of this new family is also determined.

Full-rate STBC (space-time block codes) with non-vanishing determinants achieve the optimal diversity-multiplexing tradeoff but incur high decoding complexity. To permit fast decoding, Sezginer, Sari and Biglieri proposed an STBC structure with special QR decomposition characteristics. In this paper, we adopt a simplified form of this fast-decodable code structure and present a new way to optimize the code analytically. We show that the signal constellation topology (such as QAM, APSK, or PSK) has a critical impact on the existence of non-vanishing determinants of the full-rate STBC. In particular, we show for the first time that, in order for APSK-STBC to achieve non-vanishing determinant, an APSK constellation topology with constellation points lying on square grid and ring radius √m2+n2(m,n integers) needs to be used. For signal constellations with vanishing determinants, we present a methodology to analytically optimize the full-rate STBC at specific constellation dimension.