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Non-malleable codes, introduced by Dziembowski, Pietrzak and Wichs (ICS 2010), encode messages $s$ in a manner so that tampering the codeword causes the decoder to either output $s$ or a message that is independent of $s$. While this is an…
We construct an explicit family of linear rank-metric codes over any field ${\mathbb F}_h$ that enables efficient list decoding up to a fraction $\rho$ of errors in the rank metric with a rate of $1-\rho-\epsilon$, for any desired $\rho \in…
Recent theoretical developments in coset coding theory have provided continuous-valued functions which give the equivocation and maximum likelihood (ML) decoding probability of coset secrecy codes. In this work, we develop a method for…
Some new results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list size $L$. Two asymptotic regimes are considered, the fixed list-size regime, where $L$ is fixed…
We prove that Reed-Solomon (RS) codes with random evaluation points are list recoverable up to capacity with optimal output list size, for any input list size. Namely, given an input list size $\ell$, a designated rate $R$, and any…
In a recent breakthrough [BGM23, GZ23, AGL23], it was shown that randomly punctured Reed-Solomon codes are list decodable with optimal list size with high probability, i.e., they attain the Singleton bound for list decoding [ST20, Rot22,…
We show that any q-ary code with sufficiently good distance can be randomly punctured to obtain, with high probability, a code that is list decodable up to radius $1 - 1/q - \epsilon$ with near-optimal rate and list sizes. Our results imply…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
Minimum storage regenerating codes have minimum storage of data in each node and therefore are maximal distance separable (MDS for short) codes. Thus, the number of nodes is upper bounded by $2^{\fb}$, where $\fb$ is the bits of data stored…
Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic…
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…
This paper is concerned with the ordered statistic decoding with local constraints (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly…
This paper proposes a novel maximum-likelihood (ML) soft-decision decoding framework for linear block codes, termed error-building decoding (EBD). The complete decoding process can be performed using only the parity-check matrix, without…
We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree…
In this paper, we propose a policy-guided Monte Carlo Tree Search (MCTS) decoder that achieves near maximum-likelihood decoding (MLD) performance for short block codes. The MCTS decoder searches for test error patterns (TEPs) in the…
We present a general framework for derandomizing random linear codes with respect to a broad class of properties, known as local properties, which encompass several standard notions such as distance, list-decoding, list-recovery, and…
We introduce alphabet-permutation (AP) codes, a new family of error-correcting codes defined by iteratively applying random coordinate-wise permutations to a fixed initial word. A special case recovers random additive codes and random…
An erasure code is said to be a code with sequential recovery with parameters $r$ and $t$, if for any $s \leq t$ erased code symbols, there is an $s$-step recovery process in which at each step we recover exactly one erased code symbol by…
There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - \epsilon$ is $(p,O(1/\epsilon))$-list-decodable…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…