Basis untuk Ruang Pencacah Bobot dari Kode Linier atas GF(4)

Authors

  • Intan Putri Wardani Unviversitas Nurul Jadid
  • Nur Hamid Unviversitas Nurul Jadid

Keywords:

GF(4) linear code, weight enumerator, polunomial base range

Abstract

This study discusses the basis of a polynomial space generated by the weight enumerators of linear codes over GF(4) for several lengths, namely 2, 4, 6, 8, and 10. The results of the study show that each set of weight counters forms a space with dimensions that depend on the length of the code, namely 1, 1, 2, 4, and 5. This shows that the longer the code, the larger the dimensions of the space obtained.

References

[1] MacWilliams, The Theory of Error-Correcting Codes. 1997.

[2] J. L. Butar-Butar dan M. Br. Bukit, “Metode Reversible Self-Dual untuk Konstruksi Kode DNA atas Lapangan Hingga GF(4),” Jambura J. Math, vol. 4, no. 2, hlm. 188–199, Jun 2022, doi: 10.34312/jjom.v4i2.13583.

[3] P. V, Introduction to the Theory of Error-Correcting Codes. Wiley- Interscience. 1998.

[4] V. Chauhan dan A. Sharma, “Hamming pencacah bobots of multi-twisted codes with at most two non-zero constituents,” Finite Fields and Their Applications, vol. 76, hlm. 101910, Des 2021, doi: 10.1016/j.ffa.2021.101910.

[5] I. Mukarramah dan N. Hamid, “Application of MacWilliams’ Theorem for Complete Pencacah bobots on Galois Fields”.

[6] H. and V. Pless, Fundamentals of Error-Correcting Codes. 2003.

[7] M. H. Munemasa, “Database of euclidean self-dual codes over gf(4).” 2025. [Daring]. Tersedia pada: https://www.math.is.tohoku.ac.jp/munemasa/research/codes/F4.htm [Diakses : 10 Desember 2025]

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Published

2026-06-30

How to Cite

Wardani, I. P., & Hamid, N. (2026). Basis untuk Ruang Pencacah Bobot dari Kode Linier atas GF(4) . UJMC (Unisda Journal of Mathematics and Computer Science), 12(1), 22–28. Retrieved from https://e-jurnal.unisda.ac.id/index.php/ujmc/article/view/13376

Issue

Vol. 12 No. 1 (2026): Unisda Journal of Mathematics and Computer Science

Section

Articles

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Copyright (c) 2026 UJMC (Unisda Journal of Mathematics and Computer Science)

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