Related papers: Improved decoding of affine-variety codes
We define and study a class of Reed-Muller type error-correcting codes obtained from elementary symmetric functions in finitely many variables. We determine the code parameters and higher weight spectra in the simplest cases.
We define and study a class of codes obtained from scrolls over curves of any genus over finite fields. These codes generalize Goppa codes in a natural way, and the orthogonal complements of these codes belong to the same class. We show how…
We initiate a study of locally decodable codes with randomized encoding. Standard locally decodable codes are error correcting codes with a deterministic encoding function and a randomized decoding function, such that any desired message…
Loop invariants are properties of a program loop that hold both before and after each iteration of the loop. They are often used to verify programs and ensure that algorithms consistently produce correct results during execution.…
A general class of the almost instantaneous fixed-to-variable-length (AIFV) codes is proposed, which contains every possible binary code we can make when allowing finite bits of decoding delay. The contribution of the paper lies in the…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
In this paper, we construct codes for local recovery of erasures with high availability and constant-bounded rate from the Hermitian curve. These new codes, called Hermitian-lifted codes, are evaluation codes with evaluation set being the…
A key property of an algebraic variety is whether it is absolutely irreducible, meaning that it remains irreducible over the algebraic closure of its defining field, and determining absolute irreducibility is important in algebraic geometry…
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…
In this article we extend the theory of the binary codes (the strict code $\mathcal{K}$ and the extended code $\mathcal{K}'$), associated to a projective nodal surface, to a coding theory for normal surfaces, with special consideration of…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
In this paper, we study algebraic geometry codes from curves over $\mathbb{F}_{q^\ell}$ through their virtual projections which are algebraic geometric codes over $\mathbb{F}_q$. We use the virtual projections to provide fractional decoding…
This paper presents algorithms for solving multiobjective integer programming problems. The algorithm uses Barvinok's rational functions of the polytope that defines the feasible region and provides as output the entire set of nondominated…
A new approach for decoding binary linear codes by solving a linear program (LP) over a relaxed codeword polytope was recently proposed by Feldman et al. In this paper we investigate the structure of the polytope used in the LP relaxation…
Given a completely positive map, we introduce a set of algebras that we refer to as its generalized multiplicative domains. These algebras are generalizations of the traditional multiplicative domain of a completely positive map and we…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…