arXiv subjects

Tongjiang Yan

Publications and source records attributed to Tongjiang Yan.

At least 19 recordsLinked to original sources

arXiv2026

MDS and NMDS Codes from the Extended Twisted Generalized Reed-Solomon Codes

This paper contributes to maximum distance separable (MDS) and near MDS (NMDS) properties of the extended generalized twisted Reed-Solomon (TGRS) codes. Firstly, a family of extended TGRS (ETGRS) are constructed by appending three columns to the generator matrix of original TGRS codes. Secondly, the necessary and sufficient conditions for these codes to be MDS or almost MDS (AMDS) codes are derived. Then, by analyzing the AMDS properties of their dual codes, the necessary and sufffcient conditions for them to be NMDS codes are established. Furthermore, some examples are given to verify the main results. Finally, we determine the non-generalized Reed-Solomon (non-GRS) characteristics of them via the Schur product method.

cs.IT↗

arXiv2026

Self-Orthogonal Twisted Generalized Reed-Solomon Codes and Their Application to Quantum Error-Correcting Codes

In this paper, two classes of twisted generalized Reed-Solomon (TGRS) codes with multi-twists are studied. Firstly, some sufficient and necessary conditions for these codes to be self-orthogonal and self-dual are established. Then several explicit constructions of self-orthogonal and self-dual codes are presented, from which quantum stabilizer codes are further derived. Finally, some corresponding examples are given, especially that some of these codes are MDS, AMDS or NMDS and that some of the resulting quantum stabilizer codes are optimal, achieving the quantum Singleton bound.

cs.IT↗

arXiv2025

Hermitian Self-dual Twisted Generalized Reed-Solomon Codes

Self-dual maximum distance separable (MDS) codes over finite fields are linear codes with significant combinatorial and cryptographic applications. Twisted generalized Reed-Solomon (TGRS) codes can be both MDS and self-dual. In this paper, we study a general class of TGRS codes (A-TGRS), which encompasses all previously known special cases. First, we establish a sufficient and necessary condition for an A-TGRS code to be Hermitian self-dual. Furthermore, we present four constructions of self-dual TGRS codes, which, to the best of our knowledge, nearly cover all the related results previously reported in the literature. More importantly, we also obtain several new classes of Hermitian self-dual TGRS codes with flexible parameters. Based on this framework, we derive a sufficient and necessary condition for an A-TGRS code to be Hermitian self-dual and MDS. In addition, we construct a class of MDS Hermitian self-dual TGRS code by appropriately selecting the evaluation points. This work investigates the Hermitian self-duality of TGRS codes from the perspective of matrix representation, leading to more concise and transparent analysis. More generally, the Euclidean self-dual TGRS codes and the Hermitian self-dual GRS codes can also be understood easily from this point.

cs.IT↗

arXiv2025

Construction of Self-Orthogonal Quasi-Cyclic Codes and Their Application to Quantum Error-Correcting Codes

In this paper, necessary and sufficient conditions for the self-orthogonality of t-generator quasi-cyclic (QC) codes are presented under the Euclidean, Hermitian, and symplectic inner products, respectively. Particularly, by studying the structure of the dual codes of a class of 2-generator QC codes, we derive necessary and sufficient conditions for the QC codes to be dual-containing under the above three inner products. This class of 2-generator QC codes generalizes many known codes in the literature. Based on the above conditions, we construct several quantum stabilizer codes and quantum synchronizable codes with good parameters, some of which share parameters with certain best-known codes listed in Grassl's code table.

cs.IT↗

arXiv2025

Extremal Self-Dual Codes and Linear Complementary Dual Codes from Double Circulant Codes

This paper explores extremal self-dual double circulant (DC) codes and linear complementary dual (LCD) codes of arbitrary length over the Galois field $\mathbb F_2$. We establish the sufficient and necessary conditions for DC codes and bordered DC codes to be self-dual and identify the conditions for self-dual DC codes of length up to 44 to be extremal or non-extremal. Additionally, The self-duality and extremality between DC codes and bordered DC codes are also examined. Finally, sufficient conditions for bordered DC codes to be LCD codes over $\mathbb F_2$ under Euclidean inner product are presented.

cs.IT↗

arXiv2024

Research on the Construction of Maximum Distance Separable Codes via Arbitrary twisted Generalized Reed-Solomon Codes

Maximum distance separable (MDS) codes have significant combinatorial and cryptographic applications due to their certain optimality. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Twisted generalized Reed-Solomon (TGRS) codes may not necessarily be MDS. It is meaningful to study the conditions under which TGRS codes are MDS. In this paper, we study a general class of TGRS (A-TGRS) codes which include all the known special ones. First, we obtain a new explicit expression of the inverse of the Vandermonde matrix. Based on this, we further derive an equivalent condition under which an A-TGRS code is MDS. According to this, the A-TGRS MDS codes include nearly all the known related results in the previous literatures. More importantly, we also obtain many other classes of MDS TGRS codes with new parameter matrices. In addition, we present a new method to compute the inverse of the lower triangular Toplitz matrix by a linear feedback shift register, which will be very useful in many research fields.

cs.IT↗

arXiv2022

Framework Construction of an Adversarial Federated Transfer Learning Classifier

As the Internet grows in popularity, more and more classification jobs, such as IoT, finance industry and healthcare field, rely on mobile edge computing to advance machine learning. In the medical industry, however, good diagnostic accuracy necessitates the combination of large amounts of labeled data to train the model, which is difficult and expensive to collect and risks jeopardizing patients' privacy. In this paper, we offer a novel medical diagnostic framework that employs a federated learning platform to ensure patient data privacy by transferring classification algorithms acquired in a labeled domain to a domain with sparse or missing labeled data. Rather than using a generative adversarial network, our framework uses a discriminative model to build multiple classification loss functions with the goal of improving diagnostic accuracy. It also avoids the difficulty of collecting large amounts of labeled data or the high cost of generating large amount of sample data. Experiments on real-world image datasets demonstrates that the suggested adversarial federated transfer learning method is promising for real-world medical diagnosis applications that use image classification.

cs.LG↗

arXiv2022

A new family of quantum synchronizable codes from negacyclic codes

Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, a new method for construct quantum synchronizable codes from negacyclic codes are proposed, where the length of these negacyclic codes are $p$ and $pq$. Through this method, the quantum synchronizable code possesses optimal or almost optimal error-correcting capability towards bits errors and phase errors, since the negacyclic codes we used are optimal or almost optimal. Moreover, this paper contributes to construct two classes quantum synchronizable codes, whose synchronization capabilities can reach the upper limit under certain conditions.

quant-ph↗

arXiv2021

A class of quantum synchronizable codes of length $2^n$ over ${\rm F}_q$

Quantum synchronizable codes (QSCs) are special quantum error-correcting codes which can be used to correct the effects of quantum noise on qubits and misalignment in block synchronization. In this paper, a new class of quantum synchronizable codes of length $2^n$ are constructed by using the cyclotomic cosets, whose synchronization capabilities always reach the upper bound $2^n$.

quant-ph↗

arXiv2021

Quantum Synchronizable Codes From Cyclotomic Classes of Order Two over $\mathbb{Z}_{2q}$

Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over $\mathbb{Z}_{2q}$, whose synchronization capabilities can reach the upper bound under certain conditions. Moreover, the quantum synchronizable codes possess good error-correcting capability towards bit errors and phase errors.

cs.IT↗

arXiv2021

Latency Analysis of Consortium Blockchained Federated Learning

A decentralized federated learning architecture is proposed to apply to the Businesses-to-Businesses scenarios by introducing the consortium blockchain in this paper. We introduce a model verification mechanism to ensure the quality of local models trained by participators. To analyze the latency of the system, a latency model is constructed by considering the work flow of the architecture. Finally the experiment results show that our latency model does well in quantifying the actual delays.

stat.ML↗

arXiv2021

Quantum Synchronizable Codes on Sextic Cyclotomy

Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, the quantum synchronizable codes constructed are CSS quantum error-correcting codes whose synchronization capabilities reach the upper bound. And we use cyclic codes gained by sextic cyclotomic classes to construct two classes of quantum synchronizable codes. Moreover, the quantum synchronizable codes are posses good error-correcting capability towards bit error and phase error, since the cyclic codes we used are optimal or almost optimal.

cs.CR↗

arXiv2021

Further results on the 2-adic complexity of a class of balanced generalized cyclotomic sequences

In this paper, the 2-adic complexity of a class of balanced Whiteman generalized cyclotomic sequences of period $pq$ is considered. Through calculating the determinant of the circulant matrix constructed by one of these sequences, we derive a lower bound on the 2-adic complexity of the corresponding sequence, which further expands our previous work (Zhao C, Sun Y and Yan T. Study on 2-adic complexity of a class of balanced generalized cyclotomic sequences. Journal of Cryptologic Research,6(4):455-462, 2019). The result shows that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm(RAA) for feedback with carry shift registers(FCSRs), i.e., it is in fact lower bounded by $pq-p-q-1$, which is far larger than one half of the period of the sequences. Particularly, the 2-adic complexity is maximal if suitable parameters are chosen.

cs.IT↗

arXiv2021

A new upper bound and optimal constructions of equi-difference conflict-avoiding codes on constant weight

Conflict-avoiding codes (CACs) have been used in multiple-access collision channel without feedback. The size of a CAC is the number of potential users that can be supported in the system. A code with maximum size is called optimal. The use of an optimal CAC enables the largest possible number of asynchronous users to transmit information efficiently and reliably. In this paper, a new upper bound on the maximum size of arbitrary equi-difference CAC is presented. Furthermore, three optimal constructions of equi-difference CACs are also given. One is a generalized construction for prime length $L=p$ and the other two are for two-prime length $L=pq$.

cs.IT↗

arXiv2020

The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude

In 2008, a class of binary sequences of period $N=4(2^k-1)(2^k+1)$ with optimal autocorrelation magnitude has been presented by Yu and Gong based on an $m$-sequence, the perfect sequence $(0,1,1,1)$ of period $4$ and interleaving technique. In this paper, we study the 2-adic complexities of these sequences. Our results show that they are larger than $N-2\lceil\mathrm{log}_2N\rceil+4 $ (which is far larger than $N/2$) and could attain the maximum value $N$ if suitable parameters are chosen, i.e., the 2-adic complexity of this class of interleaved sequences is large enough to resist the Rational Approximation Algorithm.

cs.IT↗

arXiv2020

Double Circulant Self-dual Codes on Sextic Cyclotomy

This paper contributes to construct double circulant self-dual codes by sextic cyclotomy. Generator matrixes of a family of pure double circulant codes and a family of double circulant codes with boundary are formed from sextic cyclotomic classes. These codes are proved to be self-dual on certain conditions. Moreover, experiments show that some of them are optimal self-dual codes or best than ever codes over GF}(2) and GF}(4).

cs.IT↗

arXiv2020

Autocorrelation and Lower Bound on the 2-Adic Complexity of LSB Sequence of $p$-ary $m$-Sequence

LSB (Least Significant Bit) sequences are widely used as the initial inputs in some modern stream ciphers, such as the ZUC algorithm-the core of the 3GPP LTE International Encryption Standard. Therefore, analyzing the statistical properties (for example, autocorrelation, linear complexity and 2-adic complexity) of these sequences becomes an important research topic. In this paper, we first reduce the autocorrelation distribution of the LSB sequence of a $p$-ary $m$-sequence with period $p^n-1$ for any order $n\geq2$ to the autocorrelation distribution of a corresponding Costas sequence with period $p-1$, and from the computing of which by computer, we obtain the explicit autocorrelation distribution of the LSB sequence for each prime $p<100$. In addition, we give a lower bound on the 2-adic complexity of each of these LSB sequences for all primes $p < 20$, which proves to be large enough to resist the analysis of RAA (Rational Approximation Algorithm) for FCSRs (Feedback with Carry Shift Registers). In particular, for a Mersenne prime $p=2^k-1$ (i.e., $k$ is a prime such that $p$ is also a prime), our results hold for all its bit-component sequences since they are shift equivalent to the LSB sequence.

cs.IT↗

arXiv2019

Double Circulant Self-Dual Codes From Generalized Cyclotomic Classes of Order Two

In this paper, constructions of some double circulant self-dual codes by generalized cyclotomic classes of order two are presented. This technique is applied to [72, 36, 12] binary highest know self-dual codes to obtain self-dual codes over GF(2) and [32, 16, 8] almost optimal self-dual codes over GF(4). Based on the properties of generalized cyclotomy, some of these codes can be proved to possess good minimum weights.

cs.IT↗