Related papers: The Generalized Covering Radii of Linear Codes
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
We introduce the concept of a sum-rank saturating system and outline its correspondence to a covering properties of a sum-rank metric code. We consider the problem of determining the shortest sum-rank-$\rho$-saturating systems of a fixed…
We present a new bound for the minimum distance of a general primary linear code. For affine variety codes defined from generalised C_{ab} curves the new bound often improves dramatically on the Feng-Rao bound for primary codes. The method…
Inspired by cartographic generalization principles, we present a generalization technique for rendering line charts at different sizes, preserving the important semantics of the data at that display size. The algorithm automatically…
Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…
Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight Griesmer $[\frac{q^k-1}{q-1},k…
The aim of this work is to algebraically describe the relative generalized Hamming weights of evaluation codes. We give a lower bound for these weights in terms of a footprint bound. We prove that this bound can be sharp. We compute the…
We obtain a classification of the completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs H(3,q) up to q and intersection array. Due to works of Meyerowitz, Mogilnykh and Valyuzenich, our result…
The generalized Hamming weight (GHW) $d_r(C)$ of linear codes $C$ is a natural generalization of the minimum Hamming distance $d(C)(=d_1(C))$ and has become one of important research objects in coding theory since Wei's originary work [23]…
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…
The capacity of a graph is defined as the rate of exponential growth of independent sets in the strong powers of the graph. In the strong power an edge connects two sequences if at each position their letters are equal or adjacent. We…
Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made…
Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to…
This paper studies a layered coding framework with a relaxed hierarchical structure. Advances in wired/wireless communication and consumer electronic devices have created a requirement for serving the same content at different quality…
The monomial codes over a Galois field F_q that can be thought invariant subspaces are essential to us in this study. More specifically, we look into the link between monomial codes and characteristic subspaces and the decomposition of…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are…
The explosion of the amount of data stored in cloud systems calls for more efficient paradigms for redundancy. While replication is widely used to ensure data availability, erasure correcting codes provide a much better trade-off between…
Many of the classic problems of coding theory are highly symmetric, which makes it easy to derive sphere-packing upper bounds and sphere-covering lower bounds on the size of codes. We discuss the generalizations of sphere-packing and…