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The recently-emerging field of higher order MDS codes has sought to unify a number of concepts in coding theory. Such areas captured by higher order MDS codes include maximally recoverable (MR) tensor codes, codes with optimal list-decoding guarantees, ...

Reed–Solomon codes are a classic family of error-correcting codes consisting of evaluations of low-degree polynomials over a finite field on some sequence of distinct field elements. They are widely known for their optimal unique-decoding capabilities, ...

DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization of its nucleotides. The formation of large stem-length secondary structures makes the sequences chemically inactive towards ...${\mathbb{}}_{\mathrm{}}$${\mathbb{}}_{\mathrm{}}$${\mathbb{}}_{\mathrm{}}$

A collection of sets displays a proximity gap with respect to some property if for every set in the collection, either (i) all members are δ-close to the property in relative Hamming distance or (ii) only a tiny fraction of members are δ-close to the ...

One main construct for code-based public key cryptosystems is the McEliece framework that hedges upon the hardness of decoding arbitrary linear codes. Based on Goppa codes, the original McEliece cryptosystem however, suffers from having very ...

In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a generalization of MDS codes. An order-ℓ MDS code, denoted by MDS(ℓ), has the property that any ℓ subspaces formed from columns of its generator matrix intersect as ...

In this article, we present an analytical model to compute the energy efficiency of underwater acoustic sensor networks (UASNs) in deep and shallow water scenarios. Acoustic parameters such as, distance-dependent usable bandwidth, acoustic fading and ...

We consider the proximity testing problem for error-correcting codes which consist in evaluations of multivariate polynomials either of bounded individual degree or bounded total degree. Namely, given an oracle function $f:L^m\to {\mathbb{F}}_q$, where $L\subset {\mathbb{F}}_q$, a ...

Low-hit-zone frequency hopping sequence (LHZ-FHS) sets having optimal Hamming correlation are desirable in quasi-synchronous communication systems. In this paper, we first derive a new bound on maximum nontrivial Hamming correlation of LHZ-FHS ...

We count the number of polynomials over finite fields with prescribed leading coefficients and a given number of linear factors. This is equivalent to counting codewords in Reed-Solomon codes which are at a certain distance from a ...

According to their strength, the tracing properties of a code can be categorized as frameproof, separating, IPP and TA. It is known that, if the minimum distance of the code is larger than a certain threshold then the TA property implies the rest. ...

We give new constructions of two classes of algebraic code families that are efficiently list decodable with small output list size from a fraction 1-R-ε of adversarial errors, where R is the rate of the code, for any desired positive constant ε. The ...

This paper presents the construction method of composite parity-check (CPC) matrices and a new burst error correcting method for (n, k) Reed-Solomon (RS) codes based on CPC matrices. The proposed method is capable of finding burst error locations by only ...

This paper proposes a distributed RS coding scheme to construct a subcode at the destination. Practically in any distributed coding scheme, an appropriate encoding strategy at the relay plays a vital role in achieving an optimized code. Therefore, ...

Reed-Solomon codes have gained a lot of interest due to its encoding simplicity, well structuredness and list-decoding capability [6] in the classical setting. This interest also translates to other metric setting, including the ...

Entanglement-assisted quantum error-correcting codes (EAQECCs) constructed from Reed–Solomon codes and BCH codes are considered in this work. It is provided a complete and explicit formula for the parameters of EAQECCs coming from any Reed–Solomon ...

Reed-Solomon (RS) codes is a popular class of codes that have been implemented in many practical systems. Recently, a fast approach to the error decoding of RS codes based on fast Fourier transform (FFT) was invented. In this work, we derive the key ...

We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed–Solomon or algebraic geometry codes, the algorithm is a reformulation of the so-called ...

In this study, the audio transmission performance of some block coding methods in wavelet and non‐wavelet cases is compared. For this purpose, a communication system has been established in the MATLAB environment for the transmission of the audio signal ...

List-decoding of Reed-Solomon (RS) codes beyond the so called Johnson radius has been one of the main open questions in coding theory and theoretical computer science since the work of Guruswami and Sudan. It is now known by the work of Rudra and ...