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All Journal Unisda Journal of Mathematics and Computer Science (UJMC)
Imamatul Mukarramah
Universitas Nurul Jadid
Computer Science & IT Education Mathematics

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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.
Co-Authors Nur Hamid