arXiv subjects

Esra Sengelen Sevim

Publications and source records attributed to Esra Sengelen Sevim.

4 recordsLinked to original sources

arXiv2017

$b$-symbol distance distribution of repeated-root cyclic codes

Symbol-pair codes, introduced by Cassuto and Blaum [1], have been raised for symbol-pair read channels. This new idea is motivated by the limitation of the reading process in high-density data storage technologies. Yaakobi et al. [8] introduced codes for $b$-symbol read channels, where the read operation is performed as a consecutive sequence of $b>2$ symbols. In this paper, we come up with a method to compute the $b$-symbol-pair distance of two $n$-tuples, where $n$ is a positive integer. Also, we deal with the $b$-symbol-pair distances of some kind of cyclic codes of length $p^e$ over $\mathbb{F}_{p^m}$.

cs.IT↗

arXiv2015

$ϕ$-classical prime submodules

In this paper, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a classical prime submodule, if for each $m\in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$ or $bm\in N$. Let $ϕ:S(M)\to S(M)\cup{\emptyset}$ be a function where $S(M)$ is the set of all submodules of $M$. We introduce the concept of "$ϕ$-classical prime submodules". A proper submodule $N$ of $M$ is a $ϕ$-classical prime submodule if whenever $a,b\in R$ and $m\in M$ with $abm\in N\backslashϕ(N)$, then $am\in N$ or $bm\in N$.

math.AC↗

arXiv2015

Some Ricci-Flat $(α,β)$-Metrics

In this paper, we study a special class of Finsler metrics, $(α,β)$-metrics, defined by $F = αϕ(\fracβα)$, where $α$ is a Riemannian metric and $β$ is a 1-form. We find an equation that characterizes Ricci-flat $(α,β)$-metrics under the condition that the length of $β$ with respect to $α$ is constant.

math.DG↗

arXiv2015

Spherically Symmetric Finsler Metrics With Constant Ricci And Flag Curvature

Spherically symmetric metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a spherically symmetric metric on R^n. In this paper, we study spherically symmetric metrics with constant Ricci curvature and constant flag curvature.

math.DG↗