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All Journal Pasundan Journal of Mathematics Education : Jurnal Pendidikan Matematika Indonesian Journal of Applied Mathematics and Statistics
Achiaa, Amma
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Computer Science & IT Decision Sciences, Operations Research & Management Education Engineering Mathematics Public Health

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Minimum Distance Computation Efficiency in Module Codes over Finite Chain Rings Meishrin, Ishlahrahmi; Sylviani, Sisilia; Achiaa, Amma
Indonesian Journal of Applied Mathematics and Statistics Vol. 2 No. 2 (2025): Indonesian Journal of Applied Mathematics and Statistics (IdJAMS)
Publisher : Lembaga Penelitian dan Pengembangan Matematika dan Statistika Terapan Indonesia, PT Anugrah Teknologi Kecerdasan Buatan PT Anugrah Teknologi Kecerdasan Buatan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.71385/idjams.v2i2.26

Abstract

In coding theory, the module structure can be used in the construction and analysis of codes for reliable data transmission. A code that is effective in detecting and correcting errors that occur during data transmission is a good code. The parameter to determine the reliability of the code in error detection and correction is by calculating its minimum distance. However, to calculate the minimum distance, it is necessary to evaluate all the Hamming weights of all non-zero code words, if the size of the code are very long, the calculation of the minimum distance will take a long time so it is not very efficient if we use this method. Therefore, the module structure of the ring, especially over the finite chain ring, can be used to simplify the calculation process of the minimum distance. The complexity of calculating the minimum distance can be reduced by viewing the code as a module and utilizing its modular structure. Previous research has shown that certain structural characteristics of module codes can significantly simplify this computation. In this article, we present an efficient method for determining the minimum distance of a module code defined over a finite chain ring. We show that it only required the hamming weight of the code generator to find the code’s minimum distance. This approach provide an efficient way to analyze the code’s reability and give algebraic insight about the code’s behaviour. Our article highlight the practical advantages of applying a module theory perspective to coding theory, which offers an efficient and theoretically grounded framework for evaluating and constructing error-correcting codes with strong performance guarantees.
Mathematical Problem-Solving Ability of Junior High School Students in Terms of Self-Directed Learning Rami, Divia Raina; Achiaa, Amma
Pasundan Journal of Mathematics Education : Jurnal Pendidikan Matematika Vol. 15 No. 2 (2025): Pasundan Journal of Mathematics Education: Jurnal Pendidikan Matematika
Publisher : Program Magister Pendidikan Matematika, Pascasarjana, Universitas Pasundan in collaboration with Asosiasi Guru Matematika Indonesia (AGMI) and Indonesian Mathematics Educators' Society (IMES)

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Abstract

Self-directed learning (SDL) is a crucial factor that can significantly improve students’ math problem-solving abilities (MPSA), particularly in 21st-century education, which emphasizes independence and critical thinking. This study aims to compare the math problem-solving abilities of junior high school students based on their self-directed learning categories. The research used a mixed-methods approach with a sequential explanatory design. It began with a quantitative phase, analyzing 82 eighth-grade students from one of the public junior high schools in West Bandung Regency through a problem-solving test and an SDL questionnaire. This was followed by a qualitative phase involving semi-structured interviews with three selected participants. The statistical results from the Welch test and Games-Howell post hoc analysis showed significant differences in math problem-solving abilities among students with high, moderate, and low SDL categories. The qualitative findings supported these results, indicating that students with high SDL were better at understanding problems, developing strategies, and reflecting independently on solutions. In contrast, students with low SDL displayed limitations in these areas. This study highlights the importance of adopting learning approaches that foster SDL in math education to enhance students’ problem-solving skills comprehensively. It also provides a theoretical contribution toward developing more adaptive, student-centered math learning strategies tailored to individual needs in 21st-century education.
Co-Authors Meishrin, Ishlahrahmi Rami, Divia Raina Sisilia Sylviani