Homogeneous Weights of Linear Codes over 𝔽pm[u, v] of Order p4m
Abstract
:1. Introduction
2. Preliminaries
3. On the Ring with Order
- (i)
- If , and where are in then this means that the cyclic code, in , is of the form
- (ii)
- If , and where and then, in , we have
- (iii)
- Assume that , and where In , we obtain
4. Matrices Associated with the MacWilliams Relation for the SWE
5. Homogeneous Weight
- H1.
- If then where
- H2.
- There is such that
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Alhomaidhi, A.A.; Alabiad, S. Homogeneous Weights of Linear Codes over 𝔽pm[u, v] of Order p4m. Symmetry 2025, 17, 440. https://doi.org/10.3390/sym17030440
Alhomaidhi AA, Alabiad S. Homogeneous Weights of Linear Codes over 𝔽pm[u, v] of Order p4m. Symmetry. 2025; 17(3):440. https://doi.org/10.3390/sym17030440
Chicago/Turabian StyleAlhomaidhi, Alhanouf Ali, and Sami Alabiad. 2025. "Homogeneous Weights of Linear Codes over 𝔽pm[u, v] of Order p4m" Symmetry 17, no. 3: 440. https://doi.org/10.3390/sym17030440
APA StyleAlhomaidhi, A. A., & Alabiad, S. (2025). Homogeneous Weights of Linear Codes over 𝔽pm[u, v] of Order p4m. Symmetry, 17(3), 440. https://doi.org/10.3390/sym17030440