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The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…
Over the past few years, the codes $\mathcal{C}_{n-1}(n,q)$ arising from the incidence of points and hyperplanes in the projective space $\text{PG}(n,q)$ attracted a lot of attention. In particular, small weight codewords of…
The hull of a linear code is defined as the intersection of the code and its dual. This concept was initially introduced to classify finite projective planes. The hull plays a crucial role in determining the complexity of algorithms used to…
Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the…
We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…
Self-dual codes over finite fields and over some finite rings have been of interest and extensively studied due to their nice algebraic structures and wide applications. Recently, characterization and enumeration of Euclidean self-dual…
This study investigates Hermitian rank-metric codes, a special class of rank-metric codes, focusing on perfect codes and on the analysis of their covering properties. Firstly, we establish bounds on the size of spheres in the space of…
Range minimum queries (RMQs) are fundamental operations with widespread applications in database management, text indexing and computational biology. While many space-efficient data structures have been designed for RMQs on arrays with…
Constructions of quantum MDS codes have been studied by many authors. We refer to the table in page 1482 of [3] for known constructions. However there are only few $q$-ary quantum MDS $[[n,n-2d+2,d]]_q$ codes with minimum distances…
Permutation decoding is a process that utilizes the permutation automorphism group of a linear code to correct errors in received words. Given a received word, a set of automorphisms, called a PD set, moves errors out of the information…
We prove that there is a Hermitian self-orthogonal $k$-dimensional truncated generalised Reed-Solomon code of length $n \leqslant q^2$ over ${\mathbb F}_{q^2}$ if and only if there is a polynomial $g \in {\mathbb F}_{q^2}$ of degree at most…
Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we…
The order bound for the minimum distance of algebraic geometry codes was originally defined for the duals of one-point codes and later generalized for arbitrary algebraic geometry codes. Another bound of order type for the minimum distance…
The main purpose of this paper is to further study the structure, parameters and constructions of the recently introduced minimal codes in the sum-rank metric. These objects form a bridge between the classical minimal codes in the Hamming…
Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this…
The task of constructing infinite families of self-dual codes with unbounded lengths and minimum distances exhibiting square-root lower bounds is extremely challenging, especially when it comes to cyclic codes. Recently, the first infinite…
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.…
Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct five new classes of $q$-ary…
We provide a geometric characterization of $k$-dimensional $\mathbb{F}_{q^m}$-linear sum-rank metric codes as tuples of $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^k$. We then use this characterization to study one-weight codes in the…