Dual Code Research Articles (Page 1)

Quantum dual extended Hamming code immune to collective coherent errors

This study aims to analyze the reception and significance of the character Gwak Bunyang in the Mongokssangbongyeonrok and GwakJangYangmunrok Series. This series is a Korean full-length novel depicting the story of Jang Hong and his descendants. Its literary and historical value is underscored by the fact that Lady Seong, a royal concubine of King Jeongjo, transcribed GwakJangYangmunrok, which enables scholars to estimate the time of its transcription and offers insight into the appreciation of Korean long novels within the royal court. The series consists of two parts: Mongokssangbongyeonrok, which centers on the heroic deeds and marriage of Jang Hong, and GwakJangYangmunrok, which focuses on the marriages of his descendants. Since Gwak Bunyang’s family is portrayed as one of the key families connected to Jang Hong and his descendants through marriage, it is essential to examine how Gwak Bunyang is depicted in the narrative. The modes of reception of Gwak Bunyang in Mongokssangbongyeonrok and GwakJangYangmunrok differ. In Mongokssangbongyeonrok, he is framed chiefly as a military hero. On the other hand, in GwakJangYangmunrok, he is cast as the head of the lineage. This contrast aligns with late-Joseon patterns of cultural enjoyment in the court and literati households. The shift visible in Gwak Bunyang Haengnakdo—from emphasizing martial prowess to highlighting prosperity and blessing—parallels the series’ separate narrativization of “heroic” and “prosperous” Gwak Bunyang. Haengnakdo was especially popular at court and among elites, a fact that resonates with the palace transcription of the Mongokssang- bongyeonrok-GwakJangYangmunrok series. This indicates that the cultural code centered on Gwak Bunyang operated not only in painting but also in narrative; the series likely mobilized that code as a narrative strategy. Whereas paintings and short fiction tend to isolate a single code, the linked form of the series keeps the “military” and “prosperity/blessing” strands apart at the work level yet integrates them as a dual code at the level of the whole. Accordingly, the series is significant not only to the history of the Korean long novel but also to broader cultural-historical currents.

ECM hybrid scaffolds decipher the dual code of organ aging

The hull of a linear code C is the intersection of C with its dual code. The goal is to study the dimensions of the hulls of optimal binary and ternary linear codes for a given length and dimension. The focus is on the lengths at which self-orthogonal (respectively, LCD) optimal codes exist at fixed dimension.

Denoising-enhanced differential chaos shift keying with joint dual orthogonal codes and time-frequency index modulation

<span lang="EN-US">This paper proposes a new approach to soft decoding for linear block codes called dual simulated annealing soft decoder (DSASD) which utilizes the dual code instead of the original code, using the <a name="_Hlk199254578"></a>simulated annealing algorithm as presented in a previously developed work. The DSASD algorithm demonstrates superior decoding performance across a wide range of codes, outperforming classical simulated annealing and several other tested decoders. We conduct a comprehensive evaluation of the proposed algorithm's performance, optimizing its parameters to achieve the best possible results. Additionally, we compare its decoding performance and algorithmic complexity with other decoding algorithms in its category. Our results demonstrate a gain in performance of approximately 2.5 dB at a bit error rate (BER) of 6×10⁻⁶ for the LDPC (60,30) code.</span>

The construction of linear codes from functions in finite fields has been widely studied in the literature. There are two generic construction methods: the first and second generic construction methods for generating linear codes from functions over finite fields. In this paper, we first define the augmented code construction of the variation of the second generic construction method and then present new infinite families of four- and five-weight self-orthogonal divisible codes derived from trace functions. Moreover, by using the augmented code construction based on the first generic construction method, we construct new infinite families of three-weight and four-weight self-orthogonal divisible codes from weakly regular plateaued functions. We determine all parameters of the constructed self-orthogonal codes as well as their dual codes over the odd characteristic finite fields. We present Hamming weights and their weight distributions for the constructed self-orthogonal codes. Additionally, we utilise the constructed p-ary self-orthogonal codes to develop p-ary Linear Complementary Dual (LCD) codes and determine the parameters of the obtained LCD codes and their dual codes.

Watermarking is a technique to help identify the source of data points, which can be used to help prevent the misuse of protected datasets. Existing methods on code watermarking, leveraging the idea from the backdoor research, embed stealthy triggers as watermarks. Despite their high resilience against dilution attacks and backdoor detections, the robustness has not been fully evaluated. To fill this gap, we propose DeCoMa , a dual-channel approach to De tect and purify Co de dataset water Ma rks. To overcome the high barrier created by the stealthy and hidden nature of code watermarks, DeCoMa leverages dual-channel constraints on code to generalize and map code samples into standardized templates. Subsequently, DeCoMa extracts hidden watermarks by identifying outlier associations between paired elements within the standardized templates. Finally, DeCoMa purifies the watermarked dataset by removing all samples containing the detected watermark, enabling the silent appropriation of protected code. We conduct extensive experiments to evaluate the effectiveness and efficiency of DeCoMa, covering 14 types of code watermarks and 3 representative intelligent code tasks (a total of 14 scenarios). Experimental results demonstrate that DeCoMa achieves a stable recall of 100% in 14 code watermark detection scenarios, significantly outperforming the baselines. Additionally, DeCoMa effectively attacks code watermarks with embedding rates as low as 0.1%, while maintaining comparable model performance after training on the purified dataset. Furthermore, as DeCoMa requires no model training for detection, it achieves substantially higher efficiency than all baselines, with a speedup ranging from 31.5 to 130.9×. The results call for more advanced watermarking techniques for code models, while DeCoMa can serve as a baseline for future evaluation.

Formally self-dual linear complementary dual codes associated with Toeplitz matrices

Linear Complementary Dual Codes Constructed from Reinforcement Learning

Construction of additive complementary dual codes over finite fields

Dual and Hull code in the first two generic constructions and relationship with the Walsh transform of cryptographic functions

In this paper, we study a type of mixed alphabet codes, called [Formula: see text]-linear codes, where [Formula: see text] with [Formula: see text]. First, we define and discuss several weight enumerators of [Formula: see text]-linear codes, including Hamming weight, Lee weight and symmetrized weight enumerators. MacWilliams identity connects the weight enumerator of codes and their dual codes. Further, we present the MacWilliams identities about Lee weight and complete weight over the ring [Formula: see text]. Finally, several examples are presented to illustrate our main results.

Let \(\mathbb{F}\)q be a finite field with q elements where q be a prime power. Among the classes of constacyclic codes of length 5ℓps over \(\mathbb{F}\)q we define an equivalence relation such that the classes of constacyclic codes which have the same structure are viewed to be equivalent. In this paper we classify the classes of constacyclic codes of length 5ℓ and give the explicit generator polynomials of all the constacyclic codes and their dual codes.

ERK Allosteric Activation: The Importance of Two Ordered Phosphorylation Events.

ERK, a coveted proliferation drug target, is a pivotal kinase in the Ras/ERK signaling cascade. Despite this, crucial questions about its activation have not been fully explored on the foundational, conformational level. Such questions include (i)Why ERK’s activation demands dual phosphorylation; (ii)What is the role of each phosphorylation site in the activation loop; and (iii)Exactly how the (ordered) phosphorylation steps affect the conformational ensembles of the activation loop,their propensities and restriction to a narrower range favoring ERK’s catalytic action. Here we used explicit molecular dynamics simulations to study ERK’s stability and the conformational changes in different stages along the activation process. The initial monophosphorylation event elongates the activation loop to enable the successive phosphorylations, which reintroduce stability/compactness through newly formed salt bridges. The interactions formed by the monophosphorylation are site-dependent, with threonine’s phosphorylation presenting stronger electrostatic interactions compared to tyrosine’s. Dual phosphorylated ERKs revealed a compact kinase structure which allows the HRD catalytic motif to stabilize the ATP. We further observe that the hinge and the homodimerization binding site responded to a tri-state signaling code based solely on the phosphorylation degree (unphosphorylated, monophosphorylated, dual phosphorylated) of the activation loop, confirming that the activation loop can allosterically influence distant regions. Last, our findings indicate that threonine phosphorylation as the second step is necessary for ERK to become effectively activated and that activation depends on the phosphorylation order. Collectively, we offer ERK’s dual allosteric phosphorylation code in activation and explain why the phosphorylation site order is crucial.

Linear Complementary Dual Codes and Linear Complementary Pairs of AG Codes in Function Fields

On quasi-abelian codes over finite commutative chain rings and their dual codes

Hashing technology has exhibited great cross-modal retrieval potential due to its appealing retrieval efficiency and storage effectiveness. Most current supervised cross-modal retrieval methods heavily rely on accurate semantic supervision, which is intractable for annotations with ever-growing sample sizes. By comparison, the existing unsupervised methods rely on accurate sample similarity preservation strategies with intensive computational costs to compensate for the lack of semantic guidance, which causes these methods to lose the power to bridge the semantic gap. Furthermore, both kinds of approaches need to search for the nearest samples among all samples in a large search space, whose process is laborious. To address these issues, this paper proposes an unsupervised dual deep hashing (UDDH) method with semantic-index and content-code for cross-modal retrieval. Deep hashing networks are utilized to extract deep features and jointly encode the dual hashing codes in a collaborative manner with a common semantic index and modality content codes to simultaneously bridge the semantic and heterogeneous gaps for cross-modal retrieval. The dual deep hashing architecture, comprising the head code on semantic index and tail codes on modality content, enhances the efficiency for cross-modal retrieval. A query sample only needs to search for the retrieved samples with the same semantic index, thus greatly shrinking the search space and achieving superior retrieval efficiency. UDDH integrates the learning processes of deep feature extraction, binary optimization, common semantic index, and modality content code within a unified model, allowing for collaborative optimization to enhance the overall performance. Extensive experiments are conducted to demonstrate the retrieval superiority of the proposed approach over the state-of-the-art baselines.

Improved Lower Bounds on the Minimum Distances of the Dual Codes of Primitive Narrow-Sense BCH Codes