Related papers: Cyclic Orbit Flag Codes
Flag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes. In this paper we present a new contribution to the study of such codes…
In network coding a constant dimension code consists of a set of k-dimensional subspaces of F_q^n. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all…
In the network coding framework, given a prime power $q$ and the vector space $\mathbb{F}_q^n$, a constant type flag code is a set of nested sequences of $\mathbb{F}_q$-subspaces (flags) with the same increasing sequence of dimensions (the…
Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space $\mathbb{F}_q^n$, where $q$ is a prime power and $\mathbb{F}_q$, the finite field of size $q$. In this paper we study the…
Subspace codes have recently been used for error correction in random network coding. In this work, we focus on one-orbit cyclic subspace codes. If $S$ is an $\mathbb{F}_q$-subspace of $\mathbb{F}_{q^n}$, then the one-orbit cyclic subspace…
A flag is a sequence of nested subspaces of a given ambient space F_q^n over a finite field F_q. In network coding, a flag code is a set of flags, all of them with the same sequence of dimensions, the type vector. In this paper, we…
Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given…
The distance distribution of a code is the vector whose $i^\text{th}$ entry is the number of pairs of codewords with distance $i$. We investigate the structure of the distance distribution for cyclic orbit codes, which are subspace codes…
Given $\mathbb{F}_q$ the finite field with $q$ elements and an integer $n\geq 2$, a flag is a sequence of nested subspaces of $\mathbb{F}_q^n$ and a flag code is a nonempty set of flags. In this context, the distance between flags is the…
Flag codes generalize constant dimension codes by considering sequences of nested subspaces with prescribed dimensions as codewords. A comprehensive construction, which unites cyclic orbit flag codes, yields two families of flag codes on…
In network coding, a flag code is a collection of flags, that is, sequences of nested subspaces of a vector space over a finite field. Due to its definition as the sum of the corresponding subspace distances, the flag distance parameter…
In this paper we study flag codes on $\mathbb{F}_q^n$, being $\mathbb{F}_q$ the finite field with $q$ elements. Special attention is given to the connection between the parameters and properties of a flag code and the ones of a family of…
Flag codes are a class of multishot network codes comprising sequences of nested subspaces (flags) within the vector space $\mathbb{F}_q^n$, where $q$ is a prime power. In this paper, we propose a family of constructions for full flag codes…
We focus on two aspects of cyclic orbit codes: invariants under equivalence and quasi-optimality. Regarding the first aspect, we establish a connection between the codewords of a cyclic orbit code and a certain linear set on the projective…
In this paper, we study flag codes on the vector space $\mathbb{F}_q^n$, being $q$ a prime power and $\mathbb{F}_q$ the finite field of $q$ elements. More precisely, we focus on flag codes that attain the maximum possible distance (optimum…
Motzkin numbers have been widely studied since they count many different combinatorial objects. In this paper we present a new appearance of this remarkable sequence in the network coding setting through a particular case of multishot codes…
A code is said to be equidistant if the distance between any two distinct codewords of the code is the same. In this paper, we have studied equidistant single-orbit cyclic and quasi-cyclic subspace codes. The orbit code generated by a…
Cyclic codes are the most studied subclass of linear codes and widely used in data storage and communication systems. Many cyclic codes have optimal parameters or the best parameters known. They are divided into simple-root cyclic codes and…
In this paper we study a class of multishot network codes given by families of nested subspaces (flags) of a vector space $\mathbb{F}_q^n$, being $q$ a prime power and $\mathbb{F}_q$ the finite field of $q$ elements. In particular, we focus…
{A cyclic subspace code is a union of the orbits of subspaces contained in it. In a recent paper, Gluesing-Luerssen et al. (Des. Codes Cryptogr. 89, 447-470, 2021) showed that the study of the distance distribution of a single orbit cyclic…