Related papers: New Improvements on the Echelon-Ferrers Constructi…
We study the classical expander codes, introduced by Sipser and Spielman \cite{SS96}. Given any constants $0< \alpha, \varepsilon < 1/2$, and an arbitrary bipartite graph with $N$ vertices on the left, $M < N$ vertices on the right, and…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
It is well known that the minimum distance for linear network codes plays the same role as the minimum distance for classical error control codes. However, Yang and Yeung (2008) discovered that for nonlinear network codes, the minimum…
We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of Leverrier, Tillich and Z\'emor can correct a constant fraction of random errors with very high probability.…
Network decompositions, as introduced by Awerbuch, Luby, Goldberg, and Plotkin [FOCS'89], are one of the key algorithmic tools in distributed graph algorithms. We present an improved deterministic distributed algorithm for constructing…
Matthews and Michel investigated the minimum distances in certain algebraic-geometry codes arising from a higher degree place $P$. In terms of the Weierstrass gap sequence at $P$, they proved a bound that gives an improvement on the…
We define a class of automorphisms of rational function fields of finite characteristic and employ these to construct different types of optimal linear rank-metric codes. The first construction is of generalized Gabidulin codes over…
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…
A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform.…
In this paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously…
Some linear codes associated to maximal algebraic curves via Feng-Rao construction are investigated. In several case, these codes have better minimum distance with respect to the previously known linear codes with same length and dimension.
This paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. Several methods to compute extensions of linear codes are presented. Many codes improving the…
We construct new linear codes with high minimum distance d. In at least 12 cases these codes improve the minimum distance of the previously known best linear codes for fixed parameters n,k. Among these new codes there is an optimal ternary…
In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015codes} with an algebraic number theoretical approach that…
We consider the problem of information flow over Gaussian relay networks. Similar to the recent work by Avestimehr \emph{et al.} [1], we propose network codes that achieve up to a constant gap from the capacity of such networks. However,…
Flag codes have received a lot of attention due to its application in random network coding. In 2021, Alonso-Gonz\'{a}lez et al. constructed optimal $(n,\mathcal{A})$-Optimum distance flag codes(ODFC) for $\mathcal {A}\subseteq…
In this work codes with availability are constructed based on the cyclic \emph{locally repairable code} (LRC) construction by Tamo et al. and their extension to $(r,\rho)$-locality by Chen et al. The minimum distance of these codes is…
Based on ideas of K\"otter and Kschischang we use constant dimension subspaces as codewords in a network. We show a connection to the theory of q-analogues of a combinatorial designs, which has been studied in Braun, Kerber and Laue as a…
Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory, {54(8), 2008] that the network coding counterpart of Gabidulin codes performs…