Search Results (32)

This work proposes a lightweight biometric key-binding scheme that adapts a PUF-style challenge–response mechanism to face geometry: a two-factor password and session nonce generate random challenge points, Gray-coded Euclidean distances to facial landmarks form responses, and a random key is bound by discarding selected positions so only a reduced subset, the nonce, and a key hash are stored. At authentication, a fresh response set is compared to the subset with a Hamming-distance tolerance, and bounded local search corrects residual errors; each successful session rotates the nonce and refreshes the ephemeral key. We frame this as a conceptual exploration of an interpretable, on-device, controlled-capture design niche—a per-session nonce-driven cancelable biometric key-binding mechanism—and we quantify the resulting security–usability trade-offs. Empirically, the scheme works under stable capture conditions with carefully tuned thresholds, and it is naturally suited to tightly controlled deployments (e.g., access kiosks) where it can also incorporate user-driven micro-gestures as an extra behavioral factor. While the construction is fragile under broader variability and leans on the second factor for security, it offers an alternative to existing mechanisms and a clear niche, and we present it as a conceptual exploration showing how CRP mechanisms can inform cancelable biometrics with per-session revocability. Full article

The performance of a frequency-hopping spread-spectrum system is mainly dependent on the mathematical properties of its hopping sequences, which are designed to minimize interference between different users. The one-coincidence sequence frequency-hopping sequence (OC-FHS) set is one of the primary types, because it achieves the lowest possible values regarding Hamming auto- and cross-correlation. In this work, we propose an OC-FHS set of a prime length p and alphabet size $pq$ for two primes p and q using a block structure modulo $pq$. In particular, when $p=q$, our construction provides a significantly larger set size compared with a previously known OC-FHS set with the same length and the same alphabet size. Moreover, the set size is optimal with respect to the bound established by Cao, Ge, and Miao. This extended set size can be applied to FHMA systems that need to accommodate a large number of users. Full article

This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how Hamming distance serves as a metric for analyzing deviations in function classification. Our extensive experimental results confirm that the Hamming distance is a pivotal metric for validating nearest neighbors in the process of classifying random functions. One of the significant conclusions we arrived is that the successful classification probability decreases monotonically with the Hamming distance. However, key exceptions were found in specific classes, revealing intra-class heterogeneity. We have established that these deviations are not random but are systemic and predictable. Furthermore, we were able to quantify these irregularities, turning potential errors into manageable phenomena. The most important novelty of this work is the demarcation, for the first time to the best of our knowledge, of precise Hamming distance intervals for the classification probability. These intervals bound the possible values the probability can assume, and provide a new foundational tool for probabilistic assessment in quantum classification. Practitioners can now endorse classification results with high certainty or dismiss them with confidence. This framework can significantly enhance any quantum classification algorithm’s reliability and decision-making capability. Full article

There are several graphs naturally associated with rings. The unitary Cayley graph of a ring R is the graph with vertex set R, where two elements $x,y\in R$ are adjacent if and only if $x-y$ is a unit of R. We show that the unitary Cayley graph $C_{T_n\left(\mathbb{F}\right)}$ of the ring $T_n\left(\mathbb{F}\right)$ of all upper triangular matrices over a finite field $\mathbb{F}$ is isomorphic to a semistrong product of a complete graph and the antipodal graph of a Hamming graph. In particular, when $\left|\mathbb{F}\right|=2$, the graph $C_{T_n\left(\mathbb{F}\right)}$ has a highly symmetric structure: it is the union of $2^{n-1}$ complete bipartite graphs. Moreover, we prove that the clique number and the chromatic number of $C_{T_n\left(\mathbb{F}\right)}$ are both equal to $\left|\mathbb{F}\right|$, and we establish tight upper and lower bounds for the domination number of $C_{T_n\left(\mathbb{F}\right)}$. Full article

We investigate analog and digital pre-emphasis for ultra-high-bit-rate coherent dual-polarization 64-QAM (DP-64QAM) transmission using OptiSystem. Two representative single-wavelength configurations are studied: 64 Gbaud (600 Gb/s payload, 768 Gb/s line rate) and 100 Gbaud (1000 Gb/s payload, 1.2 Tb/s line rate). The transmitter employs raised-cosine pulse shaping (roll-off 0.1) and a 9-bit DAC, while the receiver uses a 9-bit ADC; bandwidth-limiting Bessel/Gaussian filters emulate practical transmitter (Tx) and receiver (Rx) front-end constraints. Analog pre-emphasis (APE) is realized by uploading a measured analog filter response immediately after the DAC to compensate high-frequency roll-off. Digital pre-emphasis (DPE) is implemented before the DAC as a finite-impulse-response (FIR) pre-distortion stage, with taps obtained from the measured frequency response via spectrum mirroring, inverse FFT, Hamming-window smoothing, and normalization. We compare four cases: (i) ideal reference without bandwidth limits; (ii) bandwidth-limited without pre-emphasis; (iii) APE; and (iv) DPE. Bit-error-rate–versus–optical signal-to-noise ratio (OSNR) results show that both APE and DPE substantially mitigate bandwidth-induced penalties and approach the theoretical bound, reducing the OSNR gap to 5.8 dB at 64 Gbaud and 6.6 dB at 100 Gbaud, with operation near the forward error correction (FEC) threshold ($\mathrm{BER}={10}^{-2}$). While DPE offers full programmability, it increases peak-to-average power ratio (PAPR) and may require additional gain headroom. Overall, APE provides an effective rapid-prototyping step prior to DPE deployment, confirming the feasibility of 768 Gb/s and 1.2 Tb/s DP-64QAM links with commercially realistic components, including a 150 GSa/s DAC operating at 1.5 samples/symbol for 100 Gbaud. Full article

We develop algorithms for computing permutation polynomials (PPs) using normalization, so-called F-maps and G-maps, and the Hermite criterion. This allows for a more efficient computation of PPs for larger degrees and for larger finite fields. We use this to improve some lower bounds for $M(n,D)$, the maximum number of permutations on n symbols with a pairwise Hamming distance of D. Full article

Frequency-hopping sequences are essential in frequency-hopping spread spectrum communication systems due to their strong anti-interference capabilities, low probability of interception, and high confidentiality. Existing research has predominantly focused on the periodic Hamming correlation properties of sequences, whereas the aperiodic Hamming correlation performance more accurately reflects the actual system performance. Owing to the complexity of its application scenarios and considerable research challenges, results in this area remain scarce. In this paper, we utilize exponential sums over finite fields to derive an upper bound on a hybrid incomplete exponential sum. Then, based on this upper bound, we derive bounds on the aperiodic Hamming correlation of some frequency-hopping sequence sets constructed by trace functions. Finally, by analyzing the maximum estimation error between the average and actual frequency collision numbers of such sequence sets, the validity of the derived bound is demonstrated. Full article

We consider mixed Hamming packings, addressing the maximal cardinality of codes with a minimum codeword Hamming distance. We do not rely on any algebraic structure of the alphabets. We extend known-integer linear programming models of the problem to be efficiently tractable using standard ILP solvers. This is achieved by adopting the concept of contact graphs from classical continuous sphere packing problems to the present discrete context, resulting in a reduction technique for the models which enables their efficient solution as well as their decomposition to smaller subproblems. Based on our calculations, we provide a systematic summary of all lower and upper bounds for packings in the smallest Hamming spaces. The known results are reproduced, with some bounds found to be sharp, and the upper bounds improved in some cases. Full article

Frequency-hopping multiple access is widely adopted to blunt narrow-band jamming and limit spectral disclosure in cyber–physical systems, yet its practical resilience depends on three sequence-level properties. First, balancedness guarantees that every carrier is occupied equally often, removing spectral peaks that a jammer or energy detector could exploit. Second, a wide gap between successive hops forces any interferer to re-tune after corrupting at most one symbol, thereby containing error bursts. Third, a no-hit zone (NHZ) window with a zero pairwise Hamming correlation eliminates user collisions and self-interference when chip-level timing offsets fall inside the window. This work introduces an algebraic construction that meets the full set of requirements in a single framework. By threading a permutation over an integer ring and partitioning the period into congruent sub-blocks tied to the desired NHZ width, we generate balanced wide gap no-hit zone frequency-hopping (WG-NHZ FH) sequence sets. Analytical proofs show that (i) each sequence achieves the Lempel–Greenberger bound for auto-correlation, (ii) the family and zone sizes satisfy the Ye–Fan bound with equality, (iii) the hop-to-hop distance satisfies a provable WG condition, and (iv) balancedness holds exactly for every carrier frequency. Full article

We study single-machine group green scheduling considering group setup time deterioration effects and job-processing time learning effects, where the setup time of a group is a general deterioration function on its starting setup time and the processing time of a job is a non-increasing function on its position. We focus on confirming the job schedule for each group and group schedule for minimizing the total weighted completion time. It is proved that this problem is NP-hard. According to the problem’s NP-hardness, we present some optimal properties (including lower and upper bounds) and then propose a branch-and-bound algorithm and two heuristic algorithms (including the modified Nawaz–Enscore–Ham algorithm and simulated annealing algorithm). Finally, numerical simulations are provided to indicate the effectiveness of these algorithms, which demonstrates that the branch-and-bound algorithm can solve random instances of 100 jobs and 14 groups within reasonable time and that simulated annealing is more accurate than the modified Nawaz–Enscore–Ham algorithm. Full article

In distributed systems, the dense access of wireless devices introduces significant challenges, including severe quasi-synchronous multiple access interference (MAI) and transmission security threats, which limit the effectiveness of traditional orthogonality-based spectrum control schemes. To address these challenges, this paper proposes a new block-cipher no-hit-zone (BC-NHZ) sequence-assisted spectrum control transmission scheme, aimed at enhancing privacy protection and improving overall communication capacity for distributed systems. The BC-NHZ scheme employs block cipher encryption and establishes control sequences to represent the spectrum usage scheme. Moreover, we mathematically prove that the parameters of the BC-NHZ scheme achieve optimal results with respect to the bound of the Hamming correlation. Numerical analysis and simulation results validate the practical feasibility of the BC-NHZ scheme, demonstrating its reliability to relax synchronous requirements while providing enhanced transmission privacy protection performance. Full article

Frequency-hopping sequences (FHSs) with low Hamming correlation are essential for synchronization and multiple-access communication systems. In this paper, we propose a novel construction of FHSs using generalized cyclotomy. Our results reveal that the constructed FHSs exhibit a one-coincidence property, meaning that the smallest correlation between different FHSs, aside from the trivial case, is minimized. Additionally, the new sets of FHSs achieve an optimal size in relation to a known theoretical bound. Full article

Perfect error-correcting codes allow for an optimal transmission of information while guaranteeing error correction. For this reason, proving their existence has been a classical problem in both pure mathematics and information theory. Indeed, the classification of the parameters of e-error correcting perfect codes over q-ary alphabets was a very active topic of research in the late 20th century. Consequently, all parameters of perfect e-error-correcting codes were found if $e\ge 3$, and it was conjectured that no perfect 2-error-correcting codes exist over any q-ary alphabet, where $q>3$. In the 1970s, this was proved for q a prime power, for $q=2^r{3}^s$ and for only seven other values of q. Almost 50 years later, it is surprising to note that there have been no new results in this regard and the classification of 2-error-correcting codes over non-prime power alphabets remains an open problem. In this paper, we use techniques from the resolution of the generalised Ramanujan–Nagell equation and from modern computational number theory to show that perfect 2-error-correcting codes do not exist for 172 new values of q which are not prime powers, substantially increasing the values of q which are now classified. In addition, we prove that, for any fixed value of q, there can be at most finitely many perfect 2-error-correcting codes over an alphabet of size q. Full article

Numerous applications of the Internet of Things (IoT) feature an event recognition behavior where the established Shannon capacity is not authorized to be the central performance measure. Instead, the identification capacity for such systems is considered to be an alternative metric, and has been developed in the literature. In this paper, we develop deterministic K-identification (DKI) for the binary symmetric channel (BSC) with and without a Hamming weight constraint imposed on the codewords. This channel may be of use for IoT in the context of smart system technologies, where sophisticated communication models can be reduced to a BSC for the aim of studying basic information theoretical properties. We derive inner and outer bounds on the DKI capacity of the BSC when the size of the goal message set K may grow in the codeword length n. As a major observation, we find that, for deterministic encoding, assuming that K grows exponentially in n, i.e., $K=2^{n\kappa }$, where $\kappa$ is the identification goal rate, then the number of messages that can be accurately identified grows exponentially in n, i.e., $2^{nR}$, where R is the DKI coding rate. Furthermore, the established inner and outer bound regions reflects impact of the input constraint (Hamming weight) and the channel statistics, i.e., the cross-over probability. Full article

DNA code design is a challenging problem, and it has received great attention in the literature due to its applications in DNA data storage, DNA origami, and DNA computing. The primary focus of this paper is in constructing new DNA codes using the cosets of linear codes over the ring ${\mathbb{Z}}_4$. The Hamming distance constraint, GC-content constraint, and homopolymers constraint are all considered. In this study, we consider the cosets of Simplex alpha code, Kerdock code, Preparata code, and Hadamard code. New DNA codes of lengths four, eight, sixteen, and thirty-two are constructed using a combination of an algebraic coding approach and a variable neighborhood search approach. In addition, good lower bounds for DNA codes that satisfy important constraints have been successfully established using Magma software V2.24-4 and Python 3.10 programming in our comprehensive methodology. Full article