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All Journal UNEJ e-Proceeding BAREKENG: Jurnal Ilmu Matematika dan Terapan JCES (Journal of Character Education Society) KOMIK (Konferensi Nasional Teknologi Informasi dan Komputer) Indonesian Journal of Combinatorics FIBONACCI: Jurnal Pendidikan Matematika dan Matematika Wasana Nyata Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya Telematika MKOM WASANA NYATA International Journal of Interdisciplinary Research
Putranto Hadi Utomo
Program Studi Matematika Fakultas Matematika Dan Ilmu Pengetahuan Alam Universitas Sebelas Maret Surakarta
Religion Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Physics Social Sciences Transportation Veterinary Other

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Linear Code Analysis over GR(9) Using Hamming Distance Ferry Prabowo; Santoso Budi Wiyono; Utomo, Putranto Hadi
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.
Co-Authors Adriantasari, Salsabilla Rachma Ashidiqi, Muhammad Rofi' Bowo Winarno Bowo Winarno Diari Indriati Diari Indriati Ferry Prabowo Ilham Setyawan Ispriyanto, Mochamad Raffli Martini, Titin Sri Nugroho Arif Sudibyo Octavia Devi Safitri Sunanto Rizki Eka Oktavia Santoso Budi Wiyono Titin Sri Martini Tri Atmojo Kusmayadi Tri Atmojo Kusmayadi Utami, Risma Listya Vika Yugi Kurniawan Winarno, Bowo