arXiv subjects

Zhenliang Lu

Publications and source records attributed to Zhenliang Lu.

9 recordsLinked to original sources

arXiv2026

Entanglement-Assisted Quantum Locally Recoverable Codes: Characterizations, Bounds, and Constructions

Quantum locally recoverable codes (qLRCs) allow a single qudit erasure to be corrected by accessing only a small number of other qudits. Standard CSS and Hermitian constructions, however, impose dual-containing or self-orthogonal constraints on the underlying classical codes, thereby restricting the well-structured classical LRCs (cLRCs) that can be used to construct qLRCs. To relax these constraints, we introduce entanglement-assisted quantum locally recoverable codes (EAQLRCs) by assuming that halves of the pre-shared maximally entangled pairs are noiseless. We characterize sufficient support conditions on extended stabilizers under which entanglement-assisted stabilizer codes have locality $r$ and derive a CSS-like construction from two classical codes without imposing the ordinary dual-containing condition. We further establish an upper bound on locality and a Singleton-like bound for arbitrary CSS-like EAQLRCs, and characterize the pure codes attaining equality in the latter bound. These results yield a general framework for constructing optimal pure EAQLRCs from pairs of cLRCs. Applying this framework to $\ell$-intersection pairs of MDS codes and block parity-check matrices, we obtain two families of optimal pure CSS-like EAQLRCs with flexible parameters and nontrivial localities. To the best of our knowledge, these represent the first explicit families of EAQLRCs.

cs.IT↗

arXiv2026

A framework for constructing non-GRS MDS-NMDS codes from deep holes and its application

Maximum distance separable (MDS) codes and near MDS (NMDS) codes are of particular interest in coding theory due to their optimal error-correcting capabilities and wide applications in communication, cryptography, and storage systems. A family of linear codes is called a family of non-GRS MDS-NMDS codes if for each $[n,k]_q$ code in the family, it is either an $[n,k,n-k+1]_q$ MDS code that is not monomially equivalent to any GRS code or extended GRS code, or an $[n,k,n-k]_q$ NMDS code. This paper develops a unified framework for constructing new families of non-GRS MDS-NMDS codes via deep holes. We show that, starting from a family of $[n,k]_q$ non-GRS MDS-NMDS codes with covering radius $n-k$, one can systematically obtain more $[n+1,k+1]_q$ non-GRS MDS-NMDS codes. The proposed framework is further reformulated in terms of the second kind of extended codes. This reformulation recovers a main result of Wu, Ding, and Chen (IEEE Trans. Inf. Theory, 71(1): 263-272, 2025), provides a provable reduction in the computational complexity compared with the approach of Ma, Kai, and Zhu (Finite Fields Appl., 114, 102844, 2026), and reveals additional structural properties of the resulting codes. As an application, we determine the covering radius and characterize two classes of deep holes of extended subcodes of GRS codes. By applying our framework, we obtain three new families of non-GRS MDS-NMDS codes and investigate the monomial equivalence between the resulting codes and Roth-Lempel codes.

cs.IT↗

arXiv2026

Unique Decoding of Extended Subcodes of GRS Codes Using Error-Correcting Pairs

Extended Han-Zhang codes are a class of linear codes where each code is either a non-generalized Reed-Solomon (non-GRS) maximum distance separable (MDS) code or a near MDS (NMDS) code. They have important applications in communication, cryptography, and storage systems. While many algebraic properties and explicit constructions of extended Han-Zhang codes have been well studied in the literature, their decoding has been unexplored. In this paper, we focus on their decoding problems in terms of $\ell$-error-correcting pairs ($\ell$-ECPs) and deep holes. On the one hand, we determine the existence and specific forms of their $\ell$-ECPs, and further present an explicit decoding algorithm for extended Han-Zhang codes based on these $\ell$-ECPs, which can correct up to $\ell$ errors in polynomial time, with $\ell$ about half of the minimum distance. On the other hand, we determine the covering radius of extended Han-Zhang codes and characterize two classes of their deep holes, which are closely related to the maximum-likelihood decoding method. By employing these deep holes, we also construct more non-GRS MDS codes with larger lengths and dimensions, and discuss the monomial equivalence between them and the well-known Roth-Lempel codes. Some concrete examples are also given to support these results.

cs.IT↗

arXiv2024

JUMBO: Fully Asynchronous BFT Consensus Made Truly Scalable

Recent progresses in asynchronous Byzantine fault-tolerant (BFT) consensus, e.g. Dumbo-NG (CCS' 22) and Tusk (EuroSys' 22), show promising performance through decoupling transaction dissemination and block agreement. However, when executed with a larger number $n$ of nodes, like several hundreds, they would suffer from significant degradation in performance. Their dominating scalability bottleneck is the huge authenticator complexity: each node has to multicast $\bigO(n)$ quorum certificates (QCs) and subsequently verify them for each block. This paper systematically investigates and resolves the above scalability issue. We first propose a signature-free asynchronous BFT consensus FIN-NG that adapts a recent signature-free asynchronous common subset protocol FIN (CCS' 23) into the state-of-the-art framework of concurrent broadcast and agreement. The liveness of FIN-NG relies on our non-trivial redesign of FIN's multi-valued validated Byzantine agreement towards achieving optimal quality. FIN-NG greatly improves the performance of FIN and already outperforms Dumbo-NG in most deployment settings. To further overcome the scalability limit of FIN-NG due to $\bigO(n^3)$ messages, we propose JUMBO, a scalable instantiation of Dumbo-NG, with only $\bigO(n^2)$ complexities for both authenticators and messages. We use various aggregation and dispersal techniques for QCs to significantly reduce the authenticator complexity of original Dumbo-NG implementations by up to $\bigO(n^2)$ orders. We also propose a ``fairness'' patch for JUMBO, thus preventing a flooding adversary from controlling an overwhelming portion of transactions in its output.

cs.DC↗

arXiv2024

Dumbo-NG: Fast Asynchronous BFT Consensus with Throughput-Oblivious Latency

Despite recent progresses of practical asynchronous Byzantine fault tolerant (BFT) consensus, the state-of-the-art designs still suffer from suboptimal performance. Particularly, to obtain maximum throughput, most existing protocols with guaranteed linear amortized communication complexity require each participating node to broadcast a huge batch of transactions, which dramatically sacrifices latency. Worse still, the f slowest nodes' broadcasts might never be agreed to output and thus can be censored (where f is the number of faults). Implementable mitigation to the threat either uses computationally costly threshold encryption or incurs communication blow-up, thus causing further efficiency issues. We present Dumbo-NG, a novel asynchronous BFT consensus (atomic broadcast) to solve the remaining practical issues. Its technical core is a non-trivial direct reduction from asynchronous atomic broadcast to multi-valued validated Byzantine agreement (MVBA) with quality property. Most interestingly, the new protocol structure empowers completely concurrent execution of transaction dissemination and asynchronous agreement. This brings about two benefits: (i) the throughput-latency tension is resolved to approach peak throughput with minimal increase in latency; (ii) the transactions broadcasted by any honest node can be agreed to output, thus conquering the censorship threat with no extra cost. We implement Dumbo-NG and compare it to the state-of-the-art asynchronous BFT with guaranteed censorship resilience including Dumbo (CCS'20) and Speeding-Dumbo (NDSS'22). We also apply the techniques from Speeding-Dumbo to DispersedLedger (NSDI'22) and obtain an improved variant of DispersedLedger called sDumbo-DL for comprehensive comparison. Extensive experiments reveal: Dumbo-NG realizes better peak throughput performance and its latency can almost remain stable when throughput grows.

cs.CR↗

arXiv2022

Bolt-Dumbo Transformer: Asynchronous Consensus As Fast As the Pipelined BFT

An urgent demand of deploying BFT consensus over the Internet is raised for implementing blockchain services. The deterministic (partial) synchronous protocols can be simple and fast in good network conditions, but are subject to denial-of-service when synchrony assumption fails. Asynchronous protocols, on the contrary, are robust against the adversarial network, but are substantially more complicated and slower for the inherent use of randomness. Facing the issues, optimistic asynchronous atomic broadcast ( Kursawe-Shoup, 2002; Ramasamy-Cachin, 2005) was proposed to improve the normal-case performance of the slow asynchronous consensus. They run a deterministic fastlane if the network condition remains good, and can fall back to a fully asynchronous protocol via a pace-synchronization mechanism if the fastlane fails. Unfortunately, existing pace-synchronization directly uses a heavy tool of asynchronous multi-valued validated Byzantine agreement (MVBA). We present Bolt-Dumbo Transformer (BDT), a generic framework for practical optimistic asynchronous atomic broadcast. At the core of BDT, we set forth a new fastlane abstraction that is simple and fast, while preparing honest parties to gracefully face potential fastlane failures caused by malicious leader or bad network. This enables a highly efficient pace-synchronization to handle fallback. The resulting design reduces a cumbersome MVBA to a variant of the conceptually simplest binary agreement only. Besides detailed security analyses, we also give concrete instantiations of our framework and implement them. Extensive experiments demonstrate that BDT can enjoy both the low latency of deterministic protocols (e.g. 2-chain version of HotStuff) and the robustness of state-of-the-art asynchronous protocols in practice.

cs.CR↗

arXiv2022

Efficient Asynchronous Byzantine Agreement without Private Setups

Efficient asynchronous Byzantine agreement (BA) protocols were mostly studied with private setups, e.g., pre-setup threshold cryptosystem. Challenges remain to reduce the large communication in the absence of such setups. Recently, Abraham et al. (PODC'21) presented the first asynchronous validated BA (VBA) with expected $O(n^3)$ messages and $O(1)$ rounds, relying on only public key infrastructure (PKI) setup, but the design still costs $O(λn^3 \log n)$ bits. Here $n$ is the number of parties, and $λ$ is a cryptographic security parameter. In this paper, we reduce the communication of private-setup free asynchronous BA to expected $O(λn^3)$ bits. At the core of our design, we give a systematic treatment of common randomness protocols in the asynchronous network, and proceed as: - We give an efficient reasonably fair common coin protocol in the asynchronous setting with only PKI setup. It costs only $O(λn^3)$ bits and $O(1)$ rounds, and ensures that with at least 1/3 probability, all honest parties can output a common bit that is as if randomly flipped. This directly renders more efficient private-setup free asynchronous binary agreement (ABA) with expected $O(λn^3)$ bits and $O(1)$ rounds. - Then, we lift our common coin to attain perfect agreement by using a single ABA. This gives us a reasonably fair random leader election protocol with expected $O(λn^3)$ communication and expected constant rounds. It is pluggable in all existing VBA protocols (e.g., Cachin et al., CRYPTO'01; Abraham et al., PODC'19; Lu et al., PODC'20) to remove the needed private setup or distributed key generation (DKG). As such, the communication of private-setup free VBA is reduced to expected $O(λn^3)$ bits while preserving fast termination in expected $O(1)$ rounds.

cs.CR↗

arXiv2018

One-Lee weight and two-Lee weight $\mathbb{Z}_2\mathbb{Z}_2[u]$-additive codes

In this paper, we study one-Lee weight and two-Lee weight codes over $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$, where $u^{2}=0$. Some properties of one-Lee weight $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-additive codes are given, and a complete classification of one-Lee weight $\mathbb{Z}_2\mathbb{Z}_2[u]$-additive formally self-dual codes is obtained. The structure of two-Lee weight projective $\mathbb{Z}_2\mathbb{Z}_2[u]$ codes is determined. Some optimal binary linear codes are obtained directly from one-Lee weight and two-Lee weight $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-additive codes via the extended Gray map.

math.RA↗

arXiv2015

$\mathbb{Z}_p\mathbb{Z}_p[u]$-additive codes

In this paper, we study $\mathbb{Z}_p\mathbb{Z}_p[u]$-additive codes, where $p$ is prime and $u^{2}=0$. In particular, we determine a Gray map from $ \mathbb{Z}_p\mathbb{Z}_p[u]$ to $\mathbb{Z}_p^{ α+2 β}$ and study generator and parity check matrices for these codes. We prove that a Gray map $Φ$ is a distance preserving map from ($\mathbb{Z}_p\mathbb{Z}_p[u]$,Gray distance) to ($\mathbb{Z}_p^{α+2β}$,Hamming distance), it is a weight preserving map as well. Furthermore we study the structure of $\mathbb{Z}_p\mathbb{Z}_p[u]$-additive cyclic codes.

cs.IT↗