Journal of Algebra Combinatorics Discrete Structures and Applications
,
Year 2020
Volume 7
Issue 3
https://dergipark.org.tr/en/pub/jacodesmath
The goal of this journal is to collect the most recent work on algebra, number theory and their applications and related discrete structures. In this area we are witnessing the pure algebra applied in many interesting and applicable subjects such as Algebraic Coding Theory, Cryptography, Algebraic Combinatorics, Design Theory, Graph Theory and many related structures that find applications on Communications, Computer Science and many Engineering areas. The purpose of this journal is to provide a medium for publishing original papers in pure and applied algebra.This journal is an online journal and free of charge to all parties. The papers can be accessed freelyenSun, 06 Sep 2020 00:00:00 +0300DergiParkSome results on relative dual Baer property
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/790751
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/790751
Tayyebeh AMOUZEGAR , Rachid TRİBAK Let $R$ be a ring.
In this article, we introduce and study relative dual Baer property.
We characterize $R$-modules $M$ which are $R_R$-dual Baer, where $R$ is a commutative principal ideal domain.
It is shown that over a right noetherian right hereditary ring $R$, an $R$-module $M$ is $N$-dual Baer for
all $R$-modules $N$ if and only if $M$ is an injective $R$-module.
It is also shown that for $R$-modules $M_1$, $M_2$, $\ldots$, $M_n$ such that $M_i$ is $M_j$-projective for all
$i > j \in \{1,2,\ldots, n\}$, an $R$-module $N$ is $\bigoplus_{i=1}^nM_i$-dual Baer if and only if $N$ is
$M_i$-dual Baer for all $i\in \{1,2,\ldots,n\}$.
We prove that an $R$-module $M$ is dual Baer if and only if $S=End_R(M)$ is a Baer ring
and $IM=r_M(l_S(IM))$ for every right ideal $I$ of $S$.Sun, 06 Sep 2020 00:00:00 +0300Classification of optimal quaternary Hermitian LCD codes of dimension $2$
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/790748
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/790748
Keita ISHIZUKA Hermitian linear complementary dual codes are linear codes whose intersections with their Hermitian dual codes are trivial.
The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for each length. We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension $2$. Hermitian linear complementary dual codes are linear codes whose intersections with their Hermitian dual codes are trivial.
The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for each length. We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension $2$.Sun, 06 Sep 2020 00:00:00 +0300Generating generalized necklaces and new quasi-cyclic codes
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/784999
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/784999
Rumen DASKALOV , Elena METODIEVA In many cases there is a need of exhaustive lists of combinatorial objects of a given type. We consider generation of all inequivalent
polynomials from which defining polynomials for constructing quasi-cyclic (QC) codes are to be chosen. Using these defining polynomials we construct 34 new good QC codes over GF(11) and 36 such codes over GF(13). In many cases there is a need of exhaustive lists of combinatorial objects of a given type. We consider generation of all inequivalent polynomials from which defining polynomials for constructing quasi-cyclic (QC) codes are to be chosen. Using these defining polynomials we construct 34 new good QC codes over GF(11) and 36 such codes over GF(13).Sun, 06 Sep 2020 00:00:00 +0300Generalization of pinching operation to binary matroids
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/784992
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/784992
Vahid GHORBANİ , Ghodratollah AZADİ , Habib AZANCHİLER In this paper, we generalize the pinching operation on two edges of graphs to binary
matroids and investigate some of its basic properties. For $n\geq 2$, the matroid that is obtained from an $n$-connected matroid by this operation is a $k$-connected matroid with $k\in\{2,3,4\}$ or is a disconnected matroid. We find conditions to guarantee this $k$. Moreover, we show that Eulerian binary matroids are characterized by this operation and we also provide some interesting applications of this operation.Sun, 06 Sep 2020 00:00:00 +0300Self-dual codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}$ and applications
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/784982
https://dergipark.org.tr/en/pub/jacodesmath/issue/56695/784982
Parinyawat CHOOSUWAN , Somphong JITMAN Self-dual codes over finite fields and over some finite rings have been of interest and extensively studied due to their nice algebraic structures and wide applications. Recently, characterization and enumeration of Euclidean self-dual linear codes over the ring~$\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}$ with $u^3=0$ have been established. In this paper, Hermitian self-dual linear codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}$ are studied for all square prime powers~$q$. Complete characterization and enumeration of such codes are given. Subsequently, algebraic characterization of $H$-quasi-abelian codes in $\mathbb{F}_q[G]$ is studied, where $H\leq G$ are finite abelian groups and $\mathbb{F}_q[H]$ is a principal ideal group algebra. General characterization and enumeration of $H$-quasi-abelian codes and self-dual $H$-quasi-abelian codes in $\mathbb{F}_q[G]$ are given. For the special case where the field characteristic is $3$, an explicit formula for the number of self-dual $A\times \mathbb{Z}_3$-quasi-abelian codes in $\mathbb{F}_{3^m}[A\times \mathbb{Z}_3\times B]$ is determined for all finite abelian groups $A$ and $B$ such that $3\nmid |A|$ as well as their construction. Precisely, such codes can be represented in terms of linear codes and self-dual linear codes over $\mathbb{F}_{3^m}+u\mathbb{F}_{3^m}+u^2\mathbb{F}_{3^m}$. Some illustrative examples are provided as well.Sun, 06 Sep 2020 00:00:00 +0300