相关论文: On conjugacy classes of subgroups of the general l…
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…
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…
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…
In network coding, a flag code is a set of sequences of nested subspaces of $\mathbb{F}_q^n$, being $\mathbb{F}_q$ the finite field with $q$ elements. Flag codes defined as orbits of a cyclic subgroup of the general linear group acting on…
Cyclic orbit codes are a family of constant dimension codes used for random network coding. We investigate the Pl\"ucker embedding of these codes and show how to efficiently compute the Grassmann coordinates of the code words.
Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as…
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…
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…
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…
Spread codes and cyclic orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability, transmission rate and decoding methods, but the question of how to…
We describe a simple algorithm for classifying orbits into orbit families. This algorithm works by finding patterns in the sign changes of the principal coordinates. Orbits in the logarithmic potential are studied as an application; we…
A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the…
For a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper we…
Spread codes and orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability and transmission rate, but the question of how to encode messages has not been…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…
We give a complete list of orbit codes that are generated by an irreducible cyclic group, i.e. an irreducible group having one generator. We derive some of the basic properties of these codes such as the cardinality and the minimum…
We classify the conjugacy classes of p-cycles of type D in alternating groups. This finishes the open cases in arXiv:0812.4628. We also determine all the subracks of those conjugacy classes which are not of type D.
We study orbit codes in the field extension ${\mathbb F}_{q^n}$. First we show that the automorphism group of a cyclic orbit code is contained in the normalizer of the Singer subgroup if the orbit is generated by a subspace that is not…
Group network codes are a generalization of linear codes that have seen several studies over the last decade. When studying network codes, operations performed at internal network nodes called local encoding functions, are of significant…