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All Journal Unisda Journal of Mathematics and Computer Science (UJMC) Jurnal Penelitian Psikologi GUYUB: Journal of Community Engagement
Nur Hamid
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Religion Humanities Civil Engineering, Building, Construction & Architecture Computer Science & IT Economics, Econometrics & Finance Education Environmental Science Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Social Sciences Other

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Journal : Unisda Journal of Mathematics and Computer Science (UJMC)

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Application of MacWilliams' Theorem for Complete Weight Enumerators on Galois Fields Imamatul Mukarramah; Nur Hamid
UJMC (Unisda Journal of Mathematics and Computer Science) Vol 11 No 1 (2025): Unisda Journal of Mathematics and Computer Science
Publisher : Mathematics Department, Faculty of Sciences and Technology Unisda Lamongan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.52166/ujmc.v11i1.10075

Abstract

This paper implements the extended MacWilliams theorem for linear codes, revisiting the MacWilliams theorem for the Complete Weight Enumerator (CWE) of codes with q = 3, 4, 5, and 7. Linear codes are a mathematical concept that can be described through the distribution of weights in each codeword. CWE serves to provide a complete representation of the symbols in each codeword. This article discusses how the MacWilliams theorem can be efficiently used to calculate the CWE of codes and optimize the design of error-correcting codes. The results of this research include the calculation of CWE for and . This study contributes theoretically to the understanding of linear code structures while opening up opportunities for the development of more efficient error-correcting code algorithms in modern communication systems.
Pencacah Bobot Lengkap dari Kode Ternari Diana Putri Prahasti; Nur Hamid
UJMC (Unisda Journal of Mathematics and Computer Science) Vol 11 No 2 (2025): Unisda Journal of Mathematics and Computer Science
Publisher : Mathematics Department, Faculty of Sciences and Technology Unisda Lamongan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.52166/ujmc.v11i2.10134

Abstract

This paper presents the explicit forms of complete weight enumerators (CWEs) for ternary self-dual codes of lengths 4, 8, 12, 16, and 20. Complete weight enumerators polynomials describe the distribution of the symbols 0, 1, and 2 in each codeword, making them essential for analyzing non-binary codes. The results focus on the complete weight enumerators polynomials that form a basis for each code. This documentation serves as a concrete reference for further research in ternary code theory.
Co-Authors Anis Fitria Anjarie Dharmastuti Diana Putri Prahasti Ikhwanul Ihsan Armalid Imamatul Mukarramah Masrufah Masrufah Mochammad Sa'id Nur Azizah Rifdatul Qomariyah Syaiful Islam