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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi E-Amal: Jurnal Pengabdian Kepada Masyarakat International Journal of Interdisciplinary Research
Santoso Budi Wiyono
Universitas Sebelas Maret
Religion Agriculture, Biological Sciences & Forestry Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Health Professions Languange, Linguistic, Communication & Media Mathematics

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PELATIHAN USAHA GUNA MENINGKATKAN PROFIT UMKM TANAMAN HIAS DAN OLEH-OLEH KHAS TAWANGMANGU DI DUSUN NGLURAH Vika Yugi Kurniawan; Sutrima Sutrima; Siswanto Siswanto; Supriyadi Wibowo; Santoso Budi Wiyono
E-Amal: Jurnal Pengabdian Kepada Masyarakat Vol 4 No 3: September-Desember 2024
Publisher : LP2M STP Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47492/eamal.v4i3.3507

Abstract

This community service program was conducted by the Pure Mathematics & Application Research Group of the Mathematics Department, FMIPA UNS, with the aim of increasing the profits of ornamental plant and local specialty product SMEs in Nglurah Village, Tawangmangu District, Karanganyar Regency. The partner in this activity is the Farmers and SMEs Association located in Nglurah Village, Tawangmangu. The main issues faced by the partner are a lack of knowledge in modern business management, branding, and digital marketing, resulting in low product competitiveness in an increasingly competitive market. The solution offered includes intensive training on product processing, branding strategies, and digital marketing. The community service was implemented through a workshop attended by 30 participants, followed by a one-month mentoring period. The methodology included a participatory approach in needs assessment, theoretical and practical training, and direct mentoring in field implementation. The results showed significant improvements in participants' understanding of business management and their ability to utilize digital media for marketing. Several participants reported increased product visibility in online markets. This program is expected to have a long-term impact on the development of SMEs in Nglurah Village.
Linear Code Analysis over GR(9) Using Hamming Distance Ferry Prabowo; Santoso Budi Wiyono; Putranto Hadi Utomo
International Journal of Interdisciplinary Research Vol. 2 No. 2 (2026): Vol 2 no 2 July 2026
Publisher : Ponpes As-Salafiyyah Asy-Syafi'iyyah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.71305/ijir.v2i2.1623

Abstract

Data transmission in digital communication systems is vulnerable to disturbances such as noise and interference, which may cause errors in the received information. Therefore, coding mechanisms are required to detect and correct such errors. This study investigates the construction of linear codes over the Galois ring of nine elements . The code is constructed as a submodule of length 4 with dimension 2 , meaning that all codewords are formed as linear combinations of two linearly independent generator vectors. Two generator matrices are employed to analyze the effect of generator structure on code performance. All generated codewords are computed and evaluated using Hamming weight and Hamming distance to determine the minimum distance. The results show that the code generated by the first generator matrix has a minimum distance 3, allowing it to detect up to two errors and correct one error. In contrast, the second generator matrix produces a code with minimum distance 2 , which can only detect a single error without a correction capability. This difference indicates that code performance is more influenced by the linear relationships among generator vectors than by the presence of zero divisors in the ring structure. This study highlights the importance of selecting appropriate generator matrices in constructing linear codes over finite rings and demonstrates the potential of Galois rings as an alternative framework in coding theory.
Construction Of Linear Codes Over The Galois Ring GR(2³) With Hamming Distance Arif Febrorianto Hidayat; Putranto Hadi Utomo; Santoso Budi Wiyono
International Journal of Interdisciplinary Research Vol. 2 No. 2 (2026): Vol 2 no 2 July 2026
Publisher : Ponpes As-Salafiyyah Asy-Syafi'iyyah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.71305/ijir.v2i2.1626

Abstract

This study focuses on the construction and analysis of linear codes over a Galois ring with eight elements, motivated by the need to develop error correcting codes beyond finite fields. The objective is to examine how the selection of generator vectors influences the minimum Hamming distance and the resulting error detection and correction capabilities. The methodology involves constructing two linear codes of length four and dimension two using different generator matrices. Codewords are generated through linear combinations of generator vectors, and the minimum Hamming distance is determined by evaluating the weights of all nonzero codewords. The results show that the first generator matrix produces a minimum distance of three, allowing the detection of up to two errors and correction of one error, while the second produces a minimum distance of two, allowing only single-error detection. The findings indicate that code performance is primarily influenced by the linear relationships among generator vectors rather than solely by the presence of zero divisors. In conclusion, careful selection of generator vectors is essential for optimizing linear codes over Galois rings and improving their performance in digital communication systems.
The Triple Total Graph of The Ring Zn Vika Yugi Kurniawan; Syaifudin Zyuhri; Santoso Budi Wiyono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41488

Abstract

Let R be a commutative ring and let Z(R) denotes the set of zero-divisors of R. The triple total graph of R, denoted by TT(R), is a simple graph whose vertex set is R∖{0}. Two distinct vertices v1 and v2 are adjacent in TT(R) if and only if v1+v2∉Z(R) and there exists v3∈R∖{0}, with v3≠v1 and v3≠v2, such that v1+v3∉Z(R),  v2+v3∉Z(R), and v1+v2+v3∈Z(R).In this paper, we investigate the structural properties of the graph TT(Zn). We show that if n is even with n 2, then TT(Zn) is an empty graph. When n is prime with 2 n 11, the graph TT(Zn) is disconnected. In contrast, for prime integers n≥ 11, the graph becomes connected with diam(TT(Zn))=2 and gr(TT(Zn))=3. Moreover, each vertex has degree n−5, implying that the graph is (n−5)-regular and consequently both Eulerian and Hamiltonian. These results illustrate how the arithmetic nature of n determines the global structure of the triple total graph.
Co-Authors Arif Febrorianto Hidayat Ferry Prabowo Putranto Hadi Utomo Siswanto Siswanto Supriyadi Wibowo Sutrima Sutrima Syaifudin Zyuhri Vika Yugi Kurniawan