Abstract
In this paper, we construct two families of linear codes over the ring \({\mathbb F}_{q}+u{\mathbb F}_{q}\) by the defining set approach, where q is a prime power and \(u^2=0\). We completely determine their Lee weight distributions, which shows that these codes have few Lee weights. Via the Gray map, we obtain a family of near Griesmer codes over \({\mathbb F}_{q}\), which is also distance-optimal, and a family of linear codes over \({\mathbb F}_{q}\), whose optimality is characterized with an explicit computable criterion using the Griesmer bound.
This work was supported by the Knowledge Innovation Program of Wuhan-Basic Research under Grant 2022010801010319, the Natural Science Foundation of Hubei Province of China under Grant 2021CFA079 and the National Natural Science Foundation of China under Grant 62072162. National Natural Science Foundation of China under Grant 12001176.
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Hu, Z., Chen, B., Li, N., Zeng, X. (2023). Two Classes of Optimal Few-Weight Codes Over \({\mathbb F}_{q}+u{\mathbb F}_{q}\). In: Mesnager, S., Zhou, Z. (eds) Arithmetic of Finite Fields. WAIFI 2022. Lecture Notes in Computer Science, vol 13638. Springer, Cham. https://doi.org/10.1007/978-3-031-22944-2_13
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DOI: https://doi.org/10.1007/978-3-031-22944-2_13
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