Related papers: Equidistant subspace codes
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…
Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\F_q^n$ with a given dimension. A computer search for large constant…
We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…
For a code $C$ in a space with maximal distance $n$, we say that $C$ has symmetric distances if its distance set $S(C)$ is symmetric with respect to $n / 2$. In this paper, we prove that if $C$ is a binary code with length $2n$, constant…
In this paper we study flag codes of maximum distance. We characterize these codes in terms of, at most, two relevant constant dimension codes naturally associated to them. We do this first for general flag codes and then particularize to…
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…
MDS convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper we introduce a class of MDS convolutional codes whose column distances reach the generalized…
Subspace codes, and in particular cyclic subspace codes, have gained significant attention in recent years due to their applications in error correction for random network coding. In this paper, we introduce a new technique for constructing…
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…
Most of the codes that have an algebraic decoding algorithm are derived from the Reed Solomon codes. They are obtained by taking equivalent codes, for example the generalized Reed Solomon codes, or by using the so-called subfield subcode…
Linear codes in the projective space $\mathbb{P}_q(n)$, the set of all subspaces of the vector space $\mathbb{F}_q^n$, were first considered by Braun, Etzion and Vardy. The Grassmannian $\mathbb{G}_q(n,k)$ is the collection of all subspaces…
Non-overlapping codes are block codes that have arisen in diverse contexts of computer science and biology. Applications typically require finding non-overlapping codes with large cardinalities, but the maximum size of non-overlapping codes…
Maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible distance from each other relative to any other…
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…
Maximum rank distance codes denoted MRD-codes are the equivalent in rank metric of MDS-codes. Given any integer $q$ power of a prime and any integer $n$ there is a family of MRD-codes of length $n$ over $\FF{q^n}$ having polynomial-time…
This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…
The sum-rank metric can be seen as a generalization of both, the rank and the Hamming metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of the required field size to construct maximum distance…
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…
A basic problem for the constant dimension subspace coding is to determine the maximal possible size A_q (n, d, k) of a set of k-dimensional subspaces in Fnq such that the subspace distance satisfies d(U, V )> or =d for any two different…
The subspace design property for additive codes is a higher-dimensional generalization of the minimum distance property. As shown recently by Brakensiek, Chen, Dhar and Zhang, it implies that the code has similar performance as random…