Related papers: Bounds on List Decoding Gabidulin Codes
Motivated by the significant performance gains which polar codes experience under successive cancellation list decoding, their scaling exponent is studied as a function of the list size. In particular, the error probability is fixed and the…
We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank…
A construction of expander codes is presented with the following three properties: (i) the codes lie close to the Singleton bound, (ii) they can be encoded in time complexity that is linear in their code length, and (iii) they have a…
We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…
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…
Under polynomial time reduction, the maximum likelihood decoding of a linear code is equivalent to computing the error distance of a received word. It is known that the decoding complexity of standard Reed-Solomon codes at certain radius is…
We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main…
A convolutional code $\C$ over $\ZZ[D]$ is a $\ZZ[D]$-submodule of $\ZZN[D]$ where $\ZZ[D]$ stands for the ring of polynomials with coefficients in $\ZZ$. In this paper, we study the list decoding problem of these codes when the…
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A class of these codes was introduced by Roth, who also…
Power decoding is a partial decoding paradigm for arbitrary algebraic geometry codes for decoding beyond half the minimum distance, which usually returns the unique closest codeword, but in rare cases fails to return anything. The original…
Lifted Reed-Solomon codes are a natural affine-invariant family of error-correcting codes which generalize Reed-Muller codes. They were known to have efficient local-testing and local-decoding algorithms (comparable to the known algorithms…
We present an explicit and efficient algebraic construction of capacity-achieving list decodable codes with both constant alphabet and constant list sizes. More specifically, for any $R \in (0,1)$ and $\epsilon>0$, we give an algebraic…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
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…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…
Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good…
We derive and investigate lower bounds for the potential energy of finite spherical point sets (spherical codes). Our bounds are optimal in the following sense -- they cannot be improved by employing polynomials of the same or lower degrees…
Upper bounds on the maximum number of minimal codewords in a binary code follow from the theory of matroids. Random coding provide lower bounds. In this paper we compare these bounds with analogous bounds for the cycle code of graphs. This…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…