data storage architects

Abstract: Leakage attacks on secret sharing schemes can be based on the exploitation of partial information about individual shares to recover the underlying secret. In coding theory, linear exact repair schemes (LERSs) allow the recovery of a codeword symbol from limited information obtained from the remaining symbols. When applied to code-based secret sharing schemes, such repair schemes can be interpreted as recovering the secret from partial information about the shares, expressed in terms of subfield symbols. Guruswami and Wootters introduced the first explicit constructions of LERSs for low-rate Reed--Solomon codes that is optimal in terms of bandwidth. In this work, we first investigate the construction and algebraic properties of LERSs, building on the Guruswami-Wootters construction. We derive new explicit repair schemes from their construction and establish structural properties of the resulting schemes. Second, we further develop a systematic computational approach based on a Gr{ö}bner bases approach to identify leakage functions associated with LERSs for arbitrary linear codes. This approach enables us to investigate the existence and structural properties of LERSs across different code families and parameter ranges. We first applied our method to Reed-Solomon codes, which gave as further insights into the algebraic structure of LERSs. Moreover, by applying our method to generalized Reed-Muller and Tamo-Barg codes, we identify several LERSs that, to the best of our knowledge, have not previously been described in the literature.

Abstract: Distributional paging seeks a polynomial-time eviction rule that competes with the optimal \emph{online} policy $\mathrm{OPT}$ when requests come from a known stochastic source. Two algorithms by Lund, Phillips, and Reingold [FOCS, 1994] are canonical. Their randomized \emph{dominating distribution} algorithm, for Markov sources, evicts a page drawn from a distribution over the cache satisfying pairwise linear inequalities; their deterministic \emph{median} algorithm, for sources with independent inter-arrival times across pages, evicts the cached page with the largest lower median of its conditional next-request time. Their original guarantees of $4$ and $5$ were recently improved to $2$ and $4$ by Pabbaraju and Vakilian [ICALP 2025]. We show that neither improved constant can be reduced in its respective source model. For Markov paging, we give two complementary factor-$2$ lower-bound constructions, each with an explicit polynomial-time dominating selector. A directed-cycle family has ratio $2k/(k+1)$, while a recurrent four-page family with cache size three has ratio $2-4\varepsilon/3$. For the independent inter-arrival model, we show that the median algorithm is not $c$-competitive for any $c<4$. These are separate results for distinct stochastic models. Matching the known upper bounds, they establish tight competitive ratios of $2$ and $4$, respectively, improving on previous lower bounds of $1.5907$ and $1.511$.

Abstract: DNA offers high-density, durable storage by encoding digital information into synthetic strands and retrieving it through sequencing. Sequence reconstruction combines noisy copies of each strand before downstream decoding. Conventional offline methods typically reconstruct completed read clusters, separating reconstruction from ongoing read collection. Streaming reconstruction offers a way to overlap evidence processing with sequencing and reduce the computation remaining before downstream decoding. We present ACOR, a streaming consensus reconstruction method that records $k$-mer transitions and boundary support in a persistent ledger, then decodes through length-constrained beam search and priority-based selection at cluster closure. Evaluation on real and simulated DNA-storage datasets showed competitive recovery. On our own short-read next-generation sequencing (NGS) wet-lab library, ACOR combined near-complete recovery with second-scale reconstruction of more than ten million reads. A smaller public benchmark was completed in a fraction of a second. Parallel ACOR achieved speedups of tens to over a thousand-fold relative to the tested serial baseline configurations. Sparse storage reduced high-context memory requirements, while parallel execution accelerated reconstruction computation. ACOR is designed for streaming readout pipelines that process assigned reads while sequencing continues.

Abstract: We prove that every nontrivial linear $[n,k]$ maximum distance separable (MDS) code over a finite field $\F_q$ of characteristic two satisfies $n\le q+1$, except in dimensions $k=3$ and $k=q-1$, where $n\le q+2$. This resolves the linear MDS conjecture in even characteristic.

Abstract: We study non-additive rank-metric codes contained in the space of symmetric matrices over a finite field. Our main focus is on symmetric $2$-codes. For odd $q$, we introduce a quotient construction for $\mathrm{Sym}_3(q)$ in which rank-one differences are described by isotropic vectors of a nondegenerate quadratic form on $\mathbb F_q^4$. This leads to a correspondence with partial ovoids of the elliptic quadric $Q^-(5,q)$. Using a construction of Cossidente and Pavese, we obtain a non-additive symmetric $2$-code in $\mathrm{Sym}_3(q)$ of cardinality $q^4+2q^3$, improving the previously known general lower bound. We also give an explicit matrix description of this family. Lastly, we present a block-based construction for symmetric $2$-codes that extends the three-dimensional improvement to all odd dimensions. In particular, for every odd $n\geq3$ and every prime power $q>2$, we obtain \begin{equation*} A_q^{\rm sym}(n,2) \ge q^{(n^2-1)/2}+q^{(n^2-3)/2}+q^{(n^2-9)/2}, \end{equation*} which is strictly larger than the maximum cardinality of an additive symmetric $2$-code with the same parameters. This yields the first infinite family (as the matrix dimension $n$ varies) of non-additive symmetric $2$-codes whose size is larger than the largest achievable size of an additive code with the same parameters; before this, such a gap had only been established for $n=3$.

Abstract: Leakage attacks on secret sharing schemes exploit partial information about individual shares to recover the underlying secret. In coding theory, linear exact repair schemes (LERSs) enable the recovery of one codeword symbol from a small amount of information obtained from the remaining symbols, provided that the code has sufficiently low rate. This can be interpreted as recovering the secret from partial information, namely subfield symbols, of the shares. Recently, a randomized construction based on subfield subcodes was proposed for constructing LERS-derived leakage attacks against Massey secret sharing schemes based on general linear codes. We extend this framework to multiple shared secrets whose corresponding shares are related through linear computations, with leakage also allowed on the computation outcomes. More precisely, we consider N secrets, of which K $\le$ N are linearly independent input values and the remaining N -K secrets are determined by linear computations on these inputs. We analyse the existence of LERS-derived leakage that exploits this structure. We first study the case of addition and then generalize our construction to arbitrary linear computations. Our analysis applies to general linear codes of length n+1 and dimension k over F\_{q^m} with k $\le$ N n/(Km), and supports arbitrary linear computations, whereas the previous subfield subcode construction only applies to k $\le$ n/m -1. Consequently, exploiting the linear relations enables LERS based leakage which extend the range of code parameters vulnerable to such attacks. Finally, identical leakage functions can arise for certain linear relations, making this a more realistic yet still potentially powerful attack model. Finally, simulations indicate that identical leakage functions can be used for certain linear relations, yielding a more realistic attack model.

Abstract: The sequence reconstruction problem for $q$-ary deletion channels, introduced by Levenshtein in 2001, concerns the minimum number of channels required to uniquely recover a transmitted sequence when each channel introduces exactly $t$ deletions. Combinatorially, it is equivalent to determining $N_q(n,d,t)$, the maximum intersection size of two $t$-deletion balls with centers at Levenshtein distance at least $d$, for $q$-ary sequences of length $n$ over the alphabet \(Σ_q=\{0,1,\dots,q-1\}\). Levenshtein solved the uncoded case $N_q(n,1,t)$ for all $n\ge t$; subsequently, Gabrys and Yaakobi determined $N_2(n,2,t)$, and Wang et al. extended the result to $N_3(n,2,t)$. In this paper, we study the problem for \(q\)-ary sequences under minimum Levenshtein distance \(d=2\) with channels that introduce exactly \(t\) deletions. We determine the exact value of \(N_q(n,2,t)\) for all \(t\ge 2, q\geq 4\), and for sufficiently large \(n\), and construct explicit pairs of sequences attaining the maximum intersection. Furthermore, for each $q\ge3$, we characterize all extremal sequence pairs. In particular, if the intersection size matches the first two terms of \(N_q(n,2,t)\), then the two center sequences must contain, at the same positions, length-5 blocks of the forms \((a,b,c,a,b)\) and \((b,a,c,b,a)\) for some distinct \(a,b,c\inΣ_q\); for \(t\ge q+2\), the exact maximum \(N_q(n,2,t)\) is attained precisely by \(2q!\) unordered pairs of sequences with a specific block structure. Asymptotically, we prove that for \(q\ge 4\) and \(t\ge 2\), \[ N_q(n,2,t)=\frac{6}{(t-2)!}n^{t-2}-\frac{3t+13}{(t-3)!}n^{t-3}+\frac{3t^2+25t+64}{4(t-4)!}n^{t-4}+O(n^{t-5}). \] Moreover, \(N_q(n,2,t)\) and \(N_{q-1}(n,2,t)\) share their first \(q-1\) terms, and for \(t\ge q\) the coefficient of \(n^{t-q}\) in their difference is \(\frac{6t-6q+5}{(t-q)!}\).

Abstract: The minimum distance and the covering radius are two fundamental properties of the code. Both have been extended: the former to the generalized Hamming weights hierarchy, and the latter to the generalized covering radii hierarchy. In both cases, the lowest level of the hierarchies corresponds to the classical minimum distance and covering radius, respectively. From a geometric point of view, the minimum distance of the code determines the packing radius, which is upper bounded by the covering radius. It was conjectured this relation extends to all other orders of the hierarchy, namely, that the generalized packing radii are upper bounded by the generalized covering radii of the same order. In this paper we prove this conjecture is true for the second order radii. We also prove the conjecture holds for all orders when the code rate is at most $3/5$. Finally, we show that for any code rate in $(0,1)$, for all sufficiently long codes the conjecture holds for all orders.