Group matrix ring codes and constructions of self-dual codes

From Springer Nature via Jisc Publications RouterHistory: received 2021-01-30, rev-recd 2021-03-13, accepted 2021-03-19, registration 2021-03-20, pub-electronic 2021-04-02, online 2021-04-02, pub-print 2023-03Publication status: PublishedIn this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring Mk(R) and the ring R, where R is the commutative Frobenius ring. We show that codes over the ring Mk(R) are one sided ideals in the group matrix ring Mk(R)G and the corresponding codes over the ring R are Gk-codes of length kn. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72, 36, 12] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type I and 4 new Type II binary [72, 36, 12] self-dual codes

Screening of polymorphisms in the folate pathway in Turkish pediatric Acute Lymphoblastic Leukemia patients

Background and aim: Folate metabolic pathway plays a significant role in leukemogenesis because of its necessity for nucleotide synthesis and DNA methylation. Folate deficiency causes DNA damage. Thus polymorphisms of folate-related genes may affect the susceptibility to childhood Acute Lymphoblastic Leukemia (ALL). MTHFR (Methylenetetrahydrofolate Reductase), DHFR (Dihydrofolate reductase), CBS (Cystathionine b-synthase) and TYMS (Thymidylate Synthase) have an important role in folate pathway because their activated variants modulate synthesis of DNA and levels of folate. In this study, we aimed to investigate whether polymorphisms in genes related to folate metabolic pathway influence the risk to childhood ALL.Subject and methods: The patient groups who were diagnosed with childhood ALL at Losante Pediatric Hematology-Oncology Hospital and healthy control groups were included in the study. MTHFR 677 CT, MTHFR 1298 A-C, CBS 844ins68, DHFR 19-bp and TYMS 1494del6 polymorphisms were screened. Genotyping of these polymorphisms was performed by Restriction Fragment Length Polymorphism (RFLP) analysis and Real Time Polymerase chain Reaction (Real Time-PCR).Results: In total, we have screened 5 polymorphisms in the studied genes. The results were compared between childhood ALL patients and healthy groups. Genotype frequencies of MTHFR 677 C-T, MTHFR 1298 A-C, CBS 844ins68 and DHFR 19-bp del were similar for childhood ALL patients and healthy groups. However, statistical results showed that TYMS 1494del6 may be associated with ALL pathogenesis (p < 0.001).Conclusion: We showed that TYMS polymorphism (rs2853542) may be associated with ALL pathogenesis. In addition, our results demonstrated that MTHFR, DHFR and CBS do not affect development of leukemia. Our study displays also importance as it is the first screening results to identify association with the studied polymorphisms in Turkish patients with childhood ALL and determination of the frequency in Turkish population

New type I binary [72,36,12][72, 36, 12] self-dual codes from M6(F2)GM_6(\mathbb{F}_2)G - Group matrix rings by a hybrid search technique based on a neighbourhood-virus optimisation algorithm

From Crossref journal articles via Jisc Publications RouterPublication status: Published<p style='text-indent:20px;'>In this paper, a new search technique based on a virus optimisation algorithm is proposed for calculating the neighbours of binary self-dual codes. The aim of this new technique is to calculate neighbours of self-dual codes without reducing the search field in the search process (this technique is known in the literature due to the computational time constraint) but still obtaining results in a reasonable time (significantly faster when compared to the standard linear computational search). We employ this new search algorithm to the well-known neighbour method and its extension, the <inline-formula><tex-math id="M1">\begin{document}$k^{th}$\end{document}</tex-math></inline-formula>-range neighbours, and search for binary <inline-formula><tex-math id="M2">\begin{document}$[72, 36, 12]$\end{document}</tex-math></inline-formula> self-dual codes. In particular, we present six generator matrices of the form <inline-formula><tex-math id="M3">\begin{document}$[I_{36} \ | \ \tau_6(v)],$\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M4">\begin{document}$I_{36}$\end{document}</tex-math></inline-formula> is the <inline-formula><tex-math id="M5">\begin{document}$36 \times 36$\end{document}</tex-math></inline-formula> identity matrix, <inline-formula><tex-math id="M6">\begin{document}$v$\end{document}</tex-math></inline-formula> is an element in the group matrix ring <inline-formula><tex-math id="M7">\begin{document}$M_6(\mathbb{F}_2)G$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$G$\end{document}</tex-math></inline-formula> is a finite group of order 6, to which we employ the proposed algorithm and search for binary <inline-formula><tex-math id="M9">\begin{document}$[72, 36, 12]$\end{document}</tex-math></inline-formula> self-dual codes directly over the finite field <inline-formula><tex-math id="M10">\begin{document}$\mathbb{F}_2$\end{document}</tex-math></inline-formula>. We construct 1471 new Type I binary <inline-formula><tex-math id="M11">\begin{document}$[72, 36, 12]$\end{document}</tex-math></inline-formula> self-dual codes with the rare parameters <inline-formula><tex-math id="M12">\begin{document}$\gamma = 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 32$\end{document}</tex-math></inline-formula> in their weight enumerators.</p&gt

A novel genetic search scheme based on nature-inspired evolutionary algorithms for binary self-dual codes

From Crossref journal articles via Jisc Publications RouterPublication status: Published<p style='text-indent:20px;'>In this paper, a genetic algorithm, one of the evolutionary algorithm optimization methods, is used for the first time for the problem of computing extremal binary self-dual codes. We present a comparison of the computational times between the genetic algorithm and a linear search for different size search spaces and show that the genetic algorithm is capable of computing binary self-dual codes significantly faster than the linear search. Moreover, by employing a known matrix construction together with the genetic algorithm, we are able to obtain new binary self-dual codes of lengths 68 and 72 in a significantly short time. In particular, we obtain 11 new binary self-dual codes of length 68 and 17 new binary self-dual codes of length 72.</p&gt

Mutation-Based Algebraic Artificial Bee Colony Algorithm for Computing the Distance of Linear Codes

This article is not available on ChesterRepFinding the minimum distance of linear codes is a non-deterministic polynomial-time-hard problem and different approaches are used in the literature to solve this problem.
 Although, some of the methods focus on finding the true distances by using exact algorithms, some of them focus on optimization algorithms to find the lower or upper bounds of the distance. In this study,
 we focus on the latter approach. We first give the swarm intelligence background of artificial bee colony algorithm, we explain the algebraic approach of such algorithm and call it the algebraic artificial bee colony algorithm (A-ABC). Moreover, we develop the A-ABC algorithm by integrating it with the algebraic differential mutation operator. We call the developed algorithm the mutation-based algebraic artificial bee colony algorithm (MBA-ABC). We apply both; the A-ABC and MBA-ABC algorithms to the problem of finding the minimum distance of linear codes. The achieved results indicate that the MBA-ABC algorithm has a superior performance when compared with the A-ABC algorithm when finding the minimum distance of Bose, Chaudhuri, and Hocquenghem (BCH) codes (a special type of linear codes)

New singly and doubly even binary [72,36,12] self-dual codes from M 2(R)G - group matrix rings

From Elsevier via Jisc Publications RouterHistory: accepted 2021-08-26, epub 2021-09-17, issued 2021-12-31Article version: AMPublication status: PublishedIn this work, we present a number of generator matrices of the form [ I 2 n | τ 2 ( v ) ] , where I 2 n is the 2 n × 2 n identity matrix, v is an element in the group matrix ring M 2 ( R ) G and where R is a finite commutative Frobenius ring and G is a finite group of order 18. We employ these generator matrices and search for binary [ 72 , 36 , 12 ] self-dual codes directly over the finite field F 2 . As a result, we find 134 Type I and 1 Type II codes of this length, with parameters in their weight enumerators that were not known in the literature before. We tabulate all of our findings

Binary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme

From Crossref journal articles via Jisc Publications RouterPublication status: Published<p style='text-indent:20px;'>We present a generator matrix of the form <inline-formula><tex-math id="M1">\begin{document}$[ \sigma(v_1) \ | \ \sigma(v_2)]$\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$v_1 \in RG$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$v_2\in RH$\end{document}</tex-math></inline-formula>, for finite groups <inline-formula><tex-math id="M4">\begin{document}$G$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$H$\end{document}</tex-math></inline-formula> of order <inline-formula><tex-math id="M6">\begin{document}$n$\end{document}</tex-math></inline-formula> for constructing self-dual codes and linear complementary dual codes over the finite Frobenius ring <inline-formula><tex-math id="M7">\begin{document}$R$\end{document}</tex-math></inline-formula>. In general, many of the constructions to produce self-dual codes forces the code to be an ideal in a group ring which implies that the code has a rich automorphism group. Unlike the traditional cases, codes constructed from the generator matrix presented here are not ideals in a group ring, which enables us to find self-dual and linear complementary dual codes that are not found using more traditional techniques. In addition to that, by using this construction, we improve <inline-formula><tex-math id="M8">\begin{document}$10$\end{document}</tex-math></inline-formula> of the previously known lower bounds on the largest minimum weights of binary linear complementary dual codes for some lengths and dimensions. We also obtain <inline-formula><tex-math id="M9">\begin{document}$82$\end{document}</tex-math></inline-formula> new binary linear complementary dual codes, <inline-formula><tex-math id="M10">\begin{document}$50$\end{document}</tex-math></inline-formula> of which are either optimal or near optimal of lengths <inline-formula><tex-math id="M11">\begin{document}$41 \leq n \leq 61$\end{document}</tex-math></inline-formula> which are new to the literature.</p&gt

DNA codes from skew dihedral group ring

From Crossref journal articles via Jisc Publications RouterPublication status: Published<p style='text-indent:20px;'>In this work, we present a matrix construction for reversible codes derived from skew dihedral group rings. By employing this matrix construction, the ring <inline-formula><tex-math id="M1">\begin{document}$\mathcal{F}_{j, k}$\end{document}</tex-math></inline-formula> and its associated Gray maps, we show how one can construct reversible codes of length <inline-formula><tex-math id="M2">\begin{document}$n2^{j+k}$\end{document}</tex-math></inline-formula> over the finite field <inline-formula><tex-math id="M3">\begin{document}$\mathbb{F}_4.$\end{document}</tex-math></inline-formula> As an application, we construct a number of DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement, and the GC-content constraints with better parameters than some good DNA codes in the literature.</p&gt