Ternary Codes Research Articles (Page 1)

BackgroundDNA cytosine modifications, including 5-methylcytosine (5mC) and 5-hydroxymethylcytosine (5hmC), are key epigenetic regulators with distinct functions. Dissecting the ternary code (C, 5mC, 5hmC) across tissues and cell types remains a critical priority due to the limitations of traditional profiling methods based on bisulfite conversion.ResultsHere, we leverage the combined bisulfite and enzymatic (bACE) conversion with the Mouse Methylation BeadChip to generate 265 base-resolution ternary-code modification maps of 5mC and 5hmC across 29 mouse tissue types spanning 8–76 weeks of age and both sexes. Our atlas reveals a complex grammar of 5hmC distribution, jointly shaped by cell mitotic activity, chromatin states, and interplay with 5mC at the same and neighboring CpG sites. Of note, we demonstrate that 5hmC significantly complements 5mC-based biomarkers in delineating cell identity in both brain and non-brain tissues. Each modification state, including 5hmC alone, accurately discriminates tissue types, enabling high-precision machine learning classification of epigenetic identity. Furthermore, the ternary methylome variations extensively implicate gene transcriptional variation, with age-related changes correlated with gene expression in a tissue-dependent manner.ConclusionsOur work reveals how tissue, sex, and age jointly govern the dynamics of the two cytosine modifications, augments the scope of DNA modification biomarker discovery, and provides a reference atlas to explore epigenetic dynamics in development and disease.Supplementary InformationThe online version contains supplementary material available at 10.1186/s13059-025-03808-y.

We introduce quasi self-dual (QSD), linear complementary dual (LCD), and additive complementary dual (ACD) codes for the symplectic inner product over a non-commutative non-unitary ring of order 9. We establish connections with symplectic–self-orthogonal and LCD ternary codes. We characterize right-symplectic ACD codes.

Optimal representation in biological systems.

ABSTRACTInformation security protection has become a fundamental issue in the human life, national security, and social stability, which is enabled through the use of multi‐responsive materials. Ideal multi‐responsive materials are operated with visible to near infrared light, exhibit large separation of absorption bands, and are functional by isomerization, posing an unmet challenge. Here, a series of visible‐light‐operated molecular photoswitches, (E)‐1‐acetyl‐2‐((4‐(diphenylamino) phenyl) imino) indolin‐3‐one, and its derivatives (PIO‐01/02/03/04/05), featuring near‐infrared second aggregation‐induced emission (AIE) and impressive acid/base‐driven switching, are constructed via twisted intramolecular charge transfer (TICT) and subsequent E/Z isomerization strategies. In addition, protonation not only endows these molecules with large separation (Δλmax) of over 100 nm, but also can be used as second independent input altering the light response. Based on calculation studies and advanced spectroscopic techniques, we provide the intricate interplay of the switching behavior of PIO‐01/02/03/04/05 on their photochemical properties. The optimized compound PIO‐01 shows significant applications in multi‐color, multi‐patterning display, transient information recording and erasing, and dual‐mode encryption‐decryption with ternary code.

Linear cyclic ternary codes defined over the Galois field GF(3) exhibit several advantages over their binary counterparts. For instance, they provide an extra option for each pulse resulting into a larger set of available codes at any given length. This paper presents a comprehensive study of classes of linear cyclic ternary codes of length 25 ≤ n ≤ 50. While binary codes have been extensively studied, the properties and applications of longer ternary codes remain less explored. This study address this gap by providing an in-depth characterization of these codes for the stated lengths. Using computational methods implemented in Magma software, a diverse set of linear cyclic ternary codes over GF(3) were generated and analyzed. The paper provides a multifaceted characterization framework that integrates algebraic, combinatorial, and geometric perspectives, offering a holistic understanding of these codes. This study contributes to the theoretical advancement of non-binary codes and their practical applications in error correction, cryptography, and communication systems.

In this study, we investigate the relationships between code parameters and lattice properties, providing new insights into the structure of ternary codes from a geometric perspective. Our findings extend the existing knowledge of ternary cyclic codes, particularly for lengths exceeding 25. We construct several new codes with favorable parameters, constructed previously unreported combinatorial designs, and characterized lattices with unique properties. The results demonstrate that ternary cyclic codes exhibit high structural regularity and often produce interesting designs and lattices with properties distinct from their binary counterparts. The research reveal strong interconnections between Coding Theory, Combinatorial Design Theory, and Lattice Theory in the context of ternary codes. We provide a multifaceted characterization framework that integrates algebraic, combinatorial, and geometric perspectives, offering a holistic understanding of these codes. This study contributes to the theoretical advancement of non-binary codes and opens new avenues for their practical applications in error correction, cryptography, and communication systems.

The problem studied in this work is to determine the higher weight spectra of the Projective Reed–Muller codes associated to the Veronese [Formula: see text]-fold [Formula: see text] in [Formula: see text], which is the image of the quadratic Veronese embedding of [Formula: see text] in [Formula: see text]. We reduce the problem to the following combinatorial problem in finite geometry: For each subset [Formula: see text] of [Formula: see text], determine the dimension of the linear subspace of [Formula: see text] generated by [Formula: see text]. We develop a systematic method to solve the latter problem. We implement the method for [Formula: see text], and use it to obtain the higher weight spectra of the associated code. The case of a general finite field [Formula: see text] will be treated in a future work.

A class of ternary codes with few weights

Big data and artificial intelligence are driving increasing demand for high-density data storage. Probe-based data storage, such as mechanical storage using an atomic force microscope tip, is a potential solution with storage densities exceeding hard disks. However, the storage medium must be modifiable on the nanoscale. While polymers are promising storage media, they face challenges with synthesis, erasing temperatures, and stability. Here, a low-cost and robust polymer system is reported that allows repeated writing, reading and erasing. The polymer is made by inverse vulcanization, providing a network of S─S bonds that can be broken and re-formed repeatedly. This property is leveraged in mechanical indentation to encode information, and thermal S─S metathesis and polymer re-flow to erase. Exquisite control of indentation depth is possible over 1-30 nm. This control enables data encoding not just as a function of the presence or absence of an indent, but also indentation depth. This ternary coding increases the data density four-fold over binary coding. Furthermore, the coding can be done at room temperature which is rare for mechanical information storage. The low cost, ease of synthesis, and dynamic S─S bonds in these polymers are a promising advance in polymer storage media for probe-based data storage.

Abstract Underwater visible light communication often faces risks such as susceptibility to external light source interference, signal distortion, and information leakage. The cuprous oxide modified gallium oxide nanorod arrays detector prepared in this study can generate bipolar photocurrents under dual‐wavelength ultraviolet light without external bias voltage. Based on it, the constructed self‐powered ultraviolet ASCII code communication system not only reduce power consumption but also significantly enhance anti‐interference capability. Furthermore, the developed solar‐blind ultraviolet AMI and HDB3 ternary code communication systems can realize non‐visible light secure communication and automatic error correction. Notably, the encrypted communication system assembled using the additive property of bipolar photocurrents can also significantly improve communication security and reliability, whose bit error rate is only 0.26‰. This achievement contributes to technical advancements in underwater channel encryption and provides valuable insights for the further application of encrypted communication coding techniques.

An always-on electrocardiogram (ECG) anomaly detector (EAD) with ultra-low power (ULP) consumption is proposed for continuous cardiac monitoring applications. The detector is featured with a 1.5-bit non-feedback delta quantizer (DQ) based feature extractor, followed by a multiplier-less convolutional neural network (CNN) engine, which eliminates the traditional high-resolution analog-to-digital converter (ADC) in conventional signal processing systems. The DQ uses a computing-in-capacitor (CIC) subtractor to quantize the sample-to-sample difference of ECG signal into 1.5-bit ternary codes, which is insensitive to low-frequency baseline wandering. The subsequent event-driven classifier is composed of a low-complexity coarse detector and a systolic-array-based CNN engine for ECG anomaly detection. The DQ and the digital CNN are fabricated in 65-nm and 180-nm CMOS technology, respectively, and the two chips are integrated on board through wire bonding. The measured detection accuracy is 90.6% ∼ 91.3% when tested on the MIT-BIH arrhythmia database, identifying three different ECG anomalies. Operating at 1 V and 1.4 V power supplies for the DQ and the digital CNN, respectively, the measured long-term average power consumption of the core circuits is 36 nW, which makes the detector among those state-of-the-art always-on cardiac anomaly detection devices with the lowest power consumption.

A note on the Assmus–Mattson theorem for some ternary codes

A computational approach to using plug-in arrays, circulant matrices, and negacirculant matrices in the construction and enumeration of extremal and near-extremal self-dual ternary codes. Isomorphism classes of such codes obtainable from orthogonal designs of dimensions 2, 4, and 8 are completely enumerated for several lengths. Additionally, partial searches are conducted for larger lengths, and weight enumerators are derived for near-extremal codes.

Absolute phase retrieval based on spatial ternary phase coding with circular fringe projection

To determine the insdel distances of linear codes is a very challenging problem. The half-Singleton bound on the insdel distances of linear codes due to Cheng-Guruswami-Haeupler-Li is a basic upper bound on the insertion-deletion error-correcting capabilities of linear codes. In this paper we give several new coordinate ordering-free and coordinate ordering-depending upper bounds for the insdel distances of linear codes. These upper bounds do not depend on dimensions of linear codes and only depend on the formations of codewords. It is shown that for many natural well-known linear codes including binary simplex codes, Kasami codes, many linear binary codes with few non-zero weights and some algebraic geometry codes, the new coordinate ordering-free upper bounds on their insdel distances are strictly smaller than the half-Singleton bound and the direct upper bound. On the other hand for many linear binary codes, the ordering-depending upper bound on their insdel distance is 2. We also give ordering-depending upper bounds on the insdel distances of some linear ternary codes with few non-zero weights and some binary and ternary algebraic geometry codes.

In 2002, P. Gaborit introduced two constructions of self-dual codes using quadratic residues, so-called pure and bordered construction, as a generalization of the Pless symmetry codes. In this paper, we further study conditions under which the pure and the bordered construction using Paley designs and Paley graphs yield self-dual codes. Special attention is given to the binary and ternary codes. Further, we construct \(t\)-designs from supports of the codewords of a particular weight in the binary and ternary codes obtained.

Sports video summarization using acoustic symmetric ternary codes and SVM

New examples of self-dual near-extremal ternary codes of length 48 derived from 2-[formula omitted] designs

Codes and pseudo-geometric designs from the ternary m-sequences with Welch-type decimation d = 2 ⋅ 3(n−1)/2 + 1

Linear ternary codes of strongly regular signed graphs