Related papers: Cyclic Orbit Codes
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…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
Dynamic unary encoding takes unary encoding to the next level. Every n-bit binary string is an encoding of dynamic unary and every n-bit binary string is encodable by dynamic unary. By utilizing both forms of unary code and a single bit of…
A new construction for constant weight codes is presented. The codes are constructed from $k$-dimensional subspaces of the vector space $\F_q^n$. These subspaces form a constant dimension code in the Grassmannian space $\cG_q(n,k)$. Some of…
In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes -- a class of linear codes -- have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic…
LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…
We improve on the lower bound of the maximum number of planes of ${\rm PG}(8,q)$ mutually intersecting in at most one point leading to the following lower bound: ${\cal A}_q(9, 4; 3) \ge q^{12}+2q^8+2q^7+q^6+q^5+q^4+1$ for constant…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
As a subclass of linear codes, cyclic codes have efficient encoding and decoding algorithms, so they are widely used in many areas such as consumer electronics, data storage systems and communication systems. In this paper, we give a…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
The ring in the title is the first non commutative ring to have been used as alphabet for block codes. The original motivation was the construction of some quaternionic modular lattices from codes. The new application is the construction of…
In this paper, we describe linear and cyclic codes over the rings of the form $R_{s,p}=\mathbb{Z}_{p}[u]/\left( f\left(u\right) /\left( u-s\right) \right)$, where $p$ is a prime number and $f\left( u\right) =u^{p}-u$, with $s\in…
Symbolic codes for rotational orbits and "islands-around-islands" are constructed for the quadratic, area-preserving Henon map. The codes are based upon continuation from an anti-integrable limit, or alternatively from the horseshoe. Given…
An $(r,M,2\delta;k)_q$ constant--dimension subspace code, $\delta >1$, is a collection $\cal C$ of $(k-1)$--dimensional projective subspaces of ${\rm PG(r-1,q)}$ such that every $(k-\delta)$--dimensional projective subspace of ${\rm…
We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration…
In this paper we propose a heuristic technique for distributing points on the surface of a unit n-dimensional Euclidean sphere, generated as the orbit of a finite cyclic subgroup of orthogonal matrices, the so called cyclic group codes.…