The I/O cost, defined as the amount of data accessed at helper nodes during the repair process, is a crucial metric for repair efficiency of Reed-Solomon (RS) codes. Recently, a formula that relates the I/O cost to the Hamming weight of some linear spaces was proposed by Liu&Zhang in TCOM-2025. In this work, we introduce an effective method for calculating the Hamming weight of such linear spaces using exponential sums. With this method, we derive lower bounds on the I/O cost for RS codes evaluated on ad-dimensional subspace of Fqℓwithr= 2 or 3 parities.We further design repair schemes for RS codes evaluated on subspaces with any parities. Whenr= 2, ℓ −d+ 1 | ℓ andr= 3,d= ℓ or ℓ−d+2 | ℓ, the I/O cost of our schemes matches the lower bound established in this work. We refer to a scheme that matches the I/O cost lower bound as an I/O-optimal repair scheme. Additionally, forr= 2 withd= ℓ, we fully determine the minimum repair bandwidth of I/O-optimal repair schemes, while forr= 3 withd= ℓ, we construct an I/O-optimal repair scheme achieving a lower repair bandwidth than previous schemes.

We present a comprehensive empirical study on how backdoor attacks affect CLIP by analyzing the representations of backdoor images. Specifically, based on the methodology of representation decomposing, image representations can be decomposed into a sum of representations across individual image patches, attention heads (AHs), and multi-layer perceptrons (MLPs) in different model layers. By examining the effect of backdoor attacks on model components, we have the following empirical findings. (1) Different backdoor attacks would infect different model components, i.e., local patch-based backdoor attacks mainly affect AHs, while global perturbation-based backdoor attacks mainly affect MLPs. (2) Infected AHs are centered on the last layer, while infected MLPs are decentralized on several late layers. (3) Not all AHs in the last layer are infected and even some AHs could still maintain the original property-specific roles (e.g., ''color" and ''location''). These observations motivate us to defend against backdoor attacks by detecting infected AHs, repairing their representations, or filtering backdoor samples with too many infected AHs, in the inference stage. Experimental results validate our empirical findings and demonstrate the effectiveness of the defense methods.

Multimodal contrastive learning models (e.g., CLIP) can learn high-quality representations from large-scale image-text datasets, while they exhibit significant vulnerabilities to backdoor attacks, raising serious safety concerns. In this paper, we reveal that CLIP's vulnerabilities primarily stem from its tendency to encode features beyond in-dataset predictive patterns, compromising its visual feature resistivity to input perturbations. This makes its encoded features highly susceptible to being reshaped by backdoor triggers. To address this challenge, we propose Repulsive Visual Prompt Tuning (RVPT), a novel defense approach that employs deep visual prompt tuning with a specially designed feature-repelling loss. Specifically, RVPT adversarially repels the encoded features from deeper layers while optimizing the standard cross-entropy loss, ensuring that only predictive features in downstream tasks are encoded, thereby enhancing CLIP’s visual feature resistivity against input perturbations and mitigating its susceptibility to backdoor attacks. Unlike existing multimodal backdoor defense methods that typically require the availability of poisoned data or involve fine-tuning the entire model, RVPT leverages few-shot downstream clean samples and only tunes a small number of parameters. Empirical results demonstrate that RVPT tunes only 0.27\% of the parameters in CLIP, yet it significantly outperforms state-of-the-art defense methods, reducing the attack success rate from 89.70\% to 2.76\% against the most advanced multimodal attacks on ImageNet and effectively generalizes its defensive capabilities across multiple datasets. Our code is available on https://anonymous.4open.science/r/rvpt-anonymous.

Node repair is a crucial problem in erasure-code-based distributed storage systems. An important metric for repair efficiency is the I/O cost, which equals the total amount of data accessed at helper nodes to repair a failed node. In this work, a general formula for computing the I/O cost of linear repair schemes is derived from a new perspective, i.e., by investigating the Hamming weight of a related linear space. Applying the formula to Reed-Solomon (RS) codes, we obtain lower bounds on the I/O cost for full-length RS codes with two and three parities. Furthermore, we build linear repair schemes for the RS codes with improved I/O cost. For full-length RS codes with two parities, our scheme meets the lower bound on the I/O cost.

In recent years, the emergence of DNA storage systems has led to a widespread interest in codes correcting insertions, deletions, and classic substitutions. Levenshtein discovered that the VT codes are capable of correcting single insertion/deletion and then extended the VT construction to single-insertion/deletion/substitution correcting codes. Inspired by this, we employ the higher-order VT syndromes, which were initially introduced for 2-insertion/deletion correction, to construct 2-insertion/deletion/substitution correcting codes with redundancy 6 log2n+8. Our key technical contributions include the formalization of sign-preserving number as a core concept in applying higher-order VT syndromes and the development of its analytical framework.

Node repair is a crucial problem in erasurecode-based distributed storage systems. An important metric for repair efficiency is the I/O cost which equals the total amount of data accessed at helper nodes to repair a failed node. In this work, a general formula for computing the I/O cost of linear repair schemes is derived from a new perspective, i.e., by investigating the Hamming weight of a related linear space. Applying the formula to Reed-Solomon (RS) codes, we obtain lower bounds on the I/O cost for full-length RS codes with two and three parities. Furthermore, we build linear repair schemes for the RS codes with improved I/O cost. For full-length RS codes with two parities, our scheme meets the lower bound on the I/O cost.

Efficient node repair is a crucial problem in erasure-code-based distributed storage systems. An important metric for repair efficiency is the$\mathbf{I}/\mathbf{O}$cost which means the amount of data accessed at helper nodes during the repair process. However, minimizing the cost might not directly correspond to an optimized unless the data reads are sequential. In this work, we construct a family of$(n,\ n-r;r^{2})$MDS array codes where each node has an uncoded and sequential-access repair scheme. We call MDS codes possessing this property as access-friendly ones which are of practical importance. Since the sequential-access repair is realized at a higher sub-packetization level, our codes reach lower cost (or bandwidth) ratio than existing access-friendly MDS codes.

In this paper, we provide non-asymptotic upper bounds on the size and average size of s-insertion s-deletion balls. As a corollary, we conclude an explicit non-asymptotic lower bound on the size of optimal s-insertionldeletion correcting code which is a strict improvement of Levenshtein's lower bound given in 2002. Particularly, in the case of single insertionldeletion, comparing with Levenshtein's bound, we reduce the gap to the maximum potential lower bound by at least 1/3.

In distributed storage, cooperative repair is to simultaneously recoverh(h> 1) node erasures by downloading data from surviving nodes as well as collaboration between thehreplacement nodes. In this work, we propose a generalized cooperative repair framework for Reed-Solomon (RS) codes with two erasures. The key idea is to construct parity-check polynomials for the two replacement nodes respectively and then reduce the repair problem to the design of a linearized permutation polynomial related to the parity-check polynomials. We provide constructions of the linearized permutation polynomial in several cases, leading to cooperative repair schemes accordingly. Compared with the schemes given by Dauet al. 2021, our schemes retain the same repair bandwidth while apply to a much wider parameter regime and need only one-round collaboration. Finally we further reduce the repair bandwidth by the lifting method for RS codes of short length.

Automotive testing is now a very competitive and rapidly evolving market. As a result, the quality of testing is a leading concern for this segment. To speed up time-to-market and ensure quality, new design-for-test (DFT) architectures, new DFT methodologies and technologies are emerging. These new DFT technologies target for higher fault coverage and lower test cost. In automotive testing, 0 DPPM (defective parts per million) is required, which is the major challenge. In this industry session, we invited three DFT experts in automotive testing to share their industrial experiences in this area.

Piggybacking design has been applied extensively in distributed storage systems in recent years, since it can reduce repair bandwidth significantly with small sub-packetization. In this work, we propose a bidirectional piggybacking design (BPD) with sub-packetization l = r, where r = n − k equals the redundancy of an [n,k] linear code. Unlike most existing piggybacking designs, there is no distinction between systematic nodes and parity nodes in BPD and the piggybacks are added bidirectionally. Consequently, BPD leads to lower average repair bandwidth than previous piggybacking designs at equal subpacketization level when r ≥ 3. However, BPD needs larger fields to maintain the MDS property. We prove two upper bounds on the field size for explicit BPD and existential constructions respectively. By computer search, our BPD can be given over a field much smaller than the proved upper bounds. As an example, we provide the BPD for the [14], [10] Reed-Solomon (RS) code over F28 and obtain approximately 50% savings in the average repair bandwidth compared with the trivial repair approach. This is the lowest repair bandwidth achieved so far for [14], [10]256RS codes with sub-packetization l ≤ 4.

Identifying the top-K flows that require much more bandwidth resources in a large-scale Software-Defined Network (SDN) is essential for many network management tasks, such as load balancing, anomaly detection, and traffic engineering. However, identifying such top-K flows is not trivial, not only because of the fluctuations in flow bandwidth requirements but also because of the combinatorial explosion of problem instance sizes. In this paper, we weaken the tradeoff between exploration and exploitation and innovatively define the online top-K flows identification problem as identifying the top-K arms in a Combinatorial Multi-Armed Bandit (CMAB) model. Then, we propose a general greedy selection mechanism with some identification strategies that focus on temporal variations in the rewards. Extensive simulation experiments based on real traffic data are conducted to evaluate the performance of different strategies. In addition, the results of numerical simulations demonstrate that our proposed greedy selection mechanism significantly outperforms existing counterparts on top-K arms identification.

Piggybacking design has been applied extensively in distributed storage systems in recent years, since it can reduce repair bandwidth significantly with small sub-packetization. In this work, a bidirectional piggybacking design (BPD) is proposed with sub-packetization$2\leq l\leq r$, where$r=n-k$equals the redundancy of an$[n,k]$linear code. Unlike most existing piggybacking designs, there is no distinction between systematic nodes and parity nodes in BPD and the piggybacks are added bidirectionally. Consequently, BPD leads to lower average repair bandwidth than previous piggybacking designs at the equal sub-packetization level. However, BPD needs larger fields to maintain the MDS property. We prove two upper bounds on the field size for explicit BPD and existential constructions, respectively. By computer search, specific BPD can be given over a field much smaller than the proved upper bounds. As examples, BPD codes with sub-packetization$l=4$based on the$[{12,8}]$and$[{14,10}]$Reed-Solomon codes are given over$\mathbb {F}_{2^{8}}$, which obtain about 16% savings in the average repair bandwidth over previous designs with$l\leq 4$.

Rack-aware regenerating codes (RRCs) achieve the optimal repair bandwidth for single node failures in the hierarchical data center where nodes are organized into racks and the intra-rack communication is cost-free. In this work, a vertical-horizontal framework is proposed for building RRCs from MDS array codes and regenerating codes (RCs). Particularly for RRCs with the minimum storage (i.e., MSRR codes), the framework is further improved to achieve lower sub-packetization. As a key for building MSRR codes, MSR codes (i.e., RCs with the minimum storage) with improved sub-packetization level are also developed. Applying the newly derived MSR codes into the vertical-horizontal framework, MSRR codes with an improved sub-packetization level are explicitly constructed, and those achieving the lowest sub-packetization by far are proved to exist over sufficiently large fields.

We study the rack-aware storage system where all storage nodes are organized in racks and within each rack the nodes can communicate freely without taxing the system bandwidth. Rack-aware regenerating codes (RRCs) were proposed for minimizing the repair bandwidth for single erasures. In the initial setting of RRCs, the repair of a single node requires the participation of all the remaining nodes in the rack containing the failed node as well as a large number of helper racks containing no failures. Consequently, the repair may be infeasible in front of multiple node failures. In this work, a relaxed repair model that can tolerate multiple node failures by simultaneously reducing the intra-rack connections and cross-rack connections is proposed. A tradeoff between the storage and repair bandwidth under the relaxed repair model is derived, and parameters of the two extreme points on the tradeoff curve are characterized for the minimum storage and minimum bandwidth respectively. Moreover, two codes corresponding to the extreme points are explicitly constructed over the fields of size comparable to the code length and with the lowest sub-packetization. Finally, for the convenience of practical use, systematic encoding processes for the two codes are also established.

We consider the rack-aware storage system where$n$nodes are organized in$\bar{n}$racks each containing$u$nodes, and any$k$nodes can retrieve the stored file. Moreover, any single node erasure can be recovered by downloading data from$\bar{d}$helper racks as well as the remaining$u-1$nodes in the same rack. Previous work mostly focuses on minimizing the cross-rack repair bandwidth under the condition$\bar{d}\geq\bar{k}$, where$\bar{k}=\lfloor\frac{k}{u}\rfloor$. However,$\bar{d}\geq\bar{k}$is not an intrinsic condition for the rack-aware storage model. Reducing$\bar{d}$can improve the repair efficiency in practice and bring more flexibility into the repair process. We establish a tradeoff between the storage overhead and cross-rack repair bandwidth for the more interesting case$\bar{d} < \bar{k}$, and explicitly construct codes with parameters lying on the tradeoff curve respectively at the minimum storage point and minimum bandwidth point. The codes are scalar or have sub-packetization$\bar{d}$, and operate over finite fields of size comparable to$n$. Moreover, they remove the restriction of MBR codes having rate less than$\frac{1}{2}$and that of high-rate MSR codes having exponential sub-packetization level.

We consider the rack-aware storage system where n= n̅u nodes are organized in n̅ racks each containing u nodes, and any k = k̅u+u0(0 ≤ u0n̅to (d̅ - k̅+ 1)⌈n̅/u-u^-0⌉⌉ where d̅ is the number of helper racks that participate in the repair process; (2) The field size is reduced to |F|>n which is almost half of the field used in Chen&Barg's construction. Besides, our code keeps the same access level as Chen&Barg's low-access construction.

An (n, k, d) cooperative regenerating code provides the optimal-bandwidth repair for any t (t > 1) node failures in a cooperative way. In particular, an MSCR (minimum storage cooperative regenerating) code retains the same storage overhead as an (n, k) MDS code. Suppose each node stores α symbols which indicates the sub-packetization level of the code. A scalar MSCR code attains the minimum sub-packetization, i.e., α = d - k + t. By now, all existing constructions of scalar MSCR codes restrict to very special parameters, eg. d = k or k = 2, etc. In a recent work, Ye and Barg construct MSCR codes for all n, k, d, t, however, their construction needs α ≈ exp(nt) which is almost infeasible in practice. In this paper, we give an explicit construction of scalar MSCR codes for all d ≥ max{2k-1-t, k}, which covers all possible parameters except the case of k ≤ d ≤ 2k - 2 - t when k <; 2k - 1 - t. Moreover, as a complementary result, for k <; d <; 2k - 2 - t we prove the nonexistence of linear scalar MSCR codes that have invariant repair spaces. Our construction and most of the previous scalar MSCR codes all have invariant repair spaces and this property is appealing in practice because of convenient repair. In this sense, this work presents an almost full description of usual scalar MSCR codes.

Suppose a database containing M records is replicated in each of N servers, and a user wants to privately retrieve one record by accessing the servers such that identity of the retrieved record is secret against any up to T servers. A scheme designed for this purpose is called a T -private information retrieval (T -PIR) scheme.In this paper we focus on the field size of T -PIR schemes. We design a general capacity-achieving T -PIR scheme whose queries are generated by using some MDS array codes. It only requires field size q≥ℓ√N, where ℓ = min {tM-2, (n - t)M-2}, t = T/gcd(N, T), n = N/gcd(N, T) and has the optimal sub-packetization NnM-2. Comparing with existing capacity-achieving T -PIR schemes, our scheme has the following advantage, that is, its field size monotonically decreases as the number of records M grows. In particular, the binary field is sufficient for building a capacity-achieving T-PIR scheme as long as M ≥ 2 + ⌈logμlog2N⌉, where μ = min{t, n - t} > 1.

For locally repairable codes (LRCs), Cadambe and Mazumdar derived the first field-dependent parameter bound, known as the C-M bound. However, the C-M bound depends on an undetermined parameter kopt(q)(n, d). In this paper, a sphere-packing approach is developed for upper bounding the parameter k for [n, k, d] linear LRCs with locality r. When restricted to the binary field, three upper bounds (i.e., Bound A, Bound B, and Bound C) are derived in an explicit form. More specifically, Bound A holds under the hypothesis that the local repair groups are disjoint and of equal size. Comparing with previous bounds obtained under the same hypothesis, Bound A either covers them as special cases or has an advantage due to its explicit form. Then, the hypothesis is removed in Bound B and Bound C. As the price for explicit form, Bound B specially holds for d ≥ 5 and Bound C for r = 2. Through specific comparisons, we show that Bound B and Bound C both tend to outperform the C-M bound, as n goes large. Moreover, a family of binary linear LRCs with d ≥ 6 attaining Bound B are constructed and later extended to a wider range of parameters by a shortening technique. Lastly, most of the bounds and constructions are extended to q-ary LRCs.

Suppose M records are replicated in N servers (each storing all M records), a user wants to privately retrieve one record by accessing the servers such that the identity of the retrieved record is secret against any up to T servers. A scheme designed for this purpose is called a T-private information retrieval (PIR) scheme. In practice, capacity-achieving and small sub-packetization are both desired for PIR schemes, because the former implies the highest download rate and the latter means simple realization. Meanwhile, sub-packetization is the key technique for achieving capacity. In this paper, we characterize the optimal sub-packetization for linear capacity-achieving T-PIR schemes. First, a lower bound on the sub-packetization L for linear capacity-achieving T-PIR schemes is proved, i.e., L ≥ dnM-1, where d = gcd(N, T) and n = N/d. Then, for general values of M and N > T ≥ 1, a linear capacity-achieving T-PIR scheme with sub-packetization dnM-1is designed. Comparing with the first capacity-achieving T-PIR scheme given by Sun and Jafar in 2016, our scheme reduces the sub-packetization from NMto the optimal and further reduces the field size by a factor of NdM-2.

Consider N servers with replicated databases containing M records. Suppose a user wants to privately retrieve one record by accessing the servers such that the identity of the retrieved record is secret against any up to T servers. A scheme designed for this purpose is called a T -private information retrieval ( T -PIR) scheme. Three indexes are concerned for PIR schemes: (1) rate, indicating the amount of retrieved information per unit of downloaded data. The highest achievable rate is characterized by the capacity; (2) sub-packetization, reflecting the implementation complexity for linear schemes; (3) field size. We consider linear schemes over a finite field. In this paper, a general T - PIR scheme simultaneously attaining the optimality of almost all of the three indexes is presented. Specifically, we design a linear capacity-achieving T-PIR scheme with sub-packetization dnM-1over a finite field \mathbbFq, q ≥ N. The sub-packetization dnM-1, where d=gcd(N, T) and n=N/d, has been proved to be optimal in our previous work. The field size is reduced by an exponential factor in our scheme comparing with existing capacity -achieving T - PIR schemes.

For binary [n, k, d] linear locally repairable codes (LRCs), two new upper bounds on k are derived. The first one applies to LRCs with disjoint local repair groups, for general values of n, d and locality r, containing some previously known bounds as special cases. The second one is based on solving an optimization problem and applies to LRCs with arbitrary structure of local repair groups. Particularly, an explicit bound is derived from the second bound when d ≥ 5. A specific comparison shows this explicit bound outperforms the Cadambe-Mazumdar bound for 5 ≤ d ≤ 8 and large values of n. Moreover, a construction of binary linear LRCs with d ≥ 6 attaining our second bound is provided.

An (r, t)-locally repairable code satisfies a property that the value at each coordinate can be recovered from t disjoint repair sets each containing at most r other coordinates. This property is extremely useful in distributed storage systems for hot data. In this paper, we propose two constructions of (r, t)-LRCs. The first one is a cyclic code of which the parity check polynomial is closely related to the trace function over finite fields. This code can achieve high availability and large minimum distance. The second one is based on the inclusion matrix of linear subspaces in Fqm. For some specific parameters, we prove that its information rate is always higher than r over r+t which was conjectured to be near to the optimal rate for (r, t)-LRCs (A. Wang and Z. Zhang, ISIT 2015). By shortening this code in a specially designed way, we obtain (r, t)-LRCs with more desirable locality r at a slight expense of information rate.

The ith coordinate of an [n, k] code is said to have locality r and availability t if there exist t disjoint groups, each containing at most r other coordinates that can together recover the value of the ith coordinate. This property is particularly useful for codes for distributed storage systems because it permits local repair of failed nodes and parallel access of hot data. In this paper, for any positive integers r and t, we construct a binary linear code of length equation which has locality r and availability t for all coordinates. Although it only achieves the trivial minimum distance (i.e. t + 1), its information rate attains equation, which is higher than that of the direct product code, the only known construction that can achieve arbitrary locality and availability.

The locally repairable code (LRC) studied in this paper is an [n, k] linear code of which the value at each coordinate can be recovered by a linear combination of at most r other coordinates. The central problem in this paper is to determine the largest possible minimum distance for LRCs. First, an integer programming-based upper bound is derived for any LRC. Then, by solving the programming problem under certain conditions, an explicit upper bound is obtained for LRCs with parameters n1> n2, where n1= ⌈(n/r + 1)⌉ and n2 = n1(r +1)-n. Finally, an explicit construction for LRCs attaining this upper bound is presented over the finite field F2m,where m ≥ n1r. Based on these r ≤ √n - 1 has been definitely determined, which is of great results, the largest possible minimum distance for all LRCs with significance in practical use.

Repair locality is a desirable property for erasure codes in distributed storage systems. Recently, different structures of local repair groups have been proposed in the definitions of repair locality. In this paper, the concept of regenerating set is introduced to characterize the local repair groups. A definition of locality r(δ-1)(i.e., locality r with repair tolerance δ - 1) under the most general structure of regenerating sets is given. All previously studied locality notions turn out to be special cases of this definition. Furthermore, three representative notions of locality proposed before are reinvestigated under the framework of regenerating sets, and their respective upper bounds on the minimum distance are reproved in a uniform and brief form. Additionally, a tighter distance bound is derived for the square code which is a class of linear codes with locality r(2)and high information rate, and an explicit code construction attaining the optimal distance bound is obtained.

In distributed storage systems, erasure codes with locality r are preferred because a coordinate can be locally repaired by accessing at most r other coordinates which in turn greatly reduces the disk I/O complexity for small r. However, the local repair may not be performed when some of the r coordinates are also erased. To overcome this problem, we propose the (r, δ)c-locality providing δ-1 nonoverlapping local repair groups of size no more than r for a coordinate. Consequently, the repair locality r can tolerate δ -1 erasures in total. We derive an upper bound on the minimum distance for any linear [n, k] code with information (r, δ)c-locality. Then, we prove existence of the codes that attain this bound when n ≥ k(r(δ - 1) + 1). Although the locality (r, δ) defined by Prakash et al. provides the same level of locality and local repair tolerance as our definition, codes with (r, δ)c-locality attaining the bound are proved to have more advantage in the minimum distance. In particular, we construct a class of codes with all symbol (r, δ)c-locality where the gain in minimum distance is Q(√r) and the information rate is close to 1.

We give an explicit construction of exact cooperative regenerating codes at the MBCR (minimum bandwidth cooperative regeneration) point. Before the paper, the only known explicit MBCR codes are given with parameters n = d + r and d = k, while our construction applies to all possible values of n, k, d, r. The code has a brief expression in the polynomial form and the data reconstruction is accomplished by bivariate polynomial interpolation. It is a scalar code and operates over a finite field of size q ≥ n. Besides, we establish several subspace properties for linear exact MBCR codes. Based on these properties we prove that linear exact MBCR codes cannot achieve repair-by-transfer.

The multiplicative property is important for a linear secret sharing scheme (LSSS) to be used in constructing a multiparty computation (MPC) protocol. In general, an LSSS has to expand its share size to obtain the multiplicative property. In this paper, with respect to an MPC problem based on connectivity of graphs we devise an ideal multiplicative LSSS, that is, the LSSS is of the multiplicative property without expanding its share size. Moreover, it provides a new class of access structures that have ideal multiplicative LSSSs.