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In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders (ISD). However, recently…
Based on the notion of supercodes, we propose a two-phase maximum-likelihood soft-decision decoding (tpMLSD) algorithm for binary linear block codes in this work. The first phase applies the Viterbi algorithm backwardly to a trellis derived…
In this paper, we extend the work of (Abbondati et al., 2024) on decoding simultaneous rational number codes by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
We combine two approaches to optimize the iterative decoding of product codes with precoded polar component codes. On one side, we generate bitwise soft messages based on the codebook probability, an approximation of an auxiliary quantity…
We formulate the classical decoding algorithm of alternant codes afresh based on interpolation as in Sudan's list decoding of Reed-Solomon codes, and thus get rid of the key equation and the linear recurring sequences in the theory. The…
This paper develops an algorithmic approach for obtaining approximate, numerical estimates of the sizes of subcodes of Reed-Muller (RM) codes, all of the codewords in which satisfy a given constraint. Our algorithm is based on a statistical…
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides…
Sum-rank-metric codes have wide applications in the multishot network coding and the distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes and their Welch-Berlekamp type decoding algorithms were proposed and studied. They…
The recently introduced polar codes constitute a breakthrough in coding theory due to their capacityachieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures…
Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning,…
As powerful pre-trained vision-language models (VLMs) like CLIP gain prominence, numerous studies have attempted to combine VLMs for downstream tasks. Among these, prompt learning has been validated as an effective method for adapting to…
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and…
Large language models often solve complex reasoning tasks more effectively with Chain-of-Thought (CoT), but at the cost of long, low-bandwidth token sequences. Humans, by contrast, often reason softly by maintaining a distribution over…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
Few-weight codes over finite chain rings are associated with combinatorial objects such as strongly regular graphs (SRGs), strongly walk-regular graphs (SWRGs) and finite geometries, and are also widely used in data storage systems and…
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…
This paper defines cyclic and minimal derivative descendants (DDs) of an extended cyclic code from the derivative of the Mattson-Solomon polynomials, respectively. First, it demonstrates that the cyclic DDs are the same extended cyclic…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…