In this paper, we first determine the weight distributions of some subfield codes $ \mathcal{C}_{f}^{(p)} $ and punctured codes $ \mathcal{C}_{f}^{*(p)} $ constructed from special functions, both of which are few-weight codes. Furthermore, we derive the parameters of their dual codes. Notably, some of these codes and their duals turn out to be optimal or almost distance-optimal. As an application, two classes of 2-designs are constructed from some codes.
Citation: Shanshan Liu, Yan Liu, Xiaoyu Yu. Weight distributions of subfield codes from special functions[J]. AIMS Mathematics, 2026, 11(1): 2797-2815. doi: 10.3934/math.2026112
In this paper, we first determine the weight distributions of some subfield codes $ \mathcal{C}_{f}^{(p)} $ and punctured codes $ \mathcal{C}_{f}^{*(p)} $ constructed from special functions, both of which are few-weight codes. Furthermore, we derive the parameters of their dual codes. Notably, some of these codes and their duals turn out to be optimal or almost distance-optimal. As an application, two classes of 2-designs are constructed from some codes.
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Shanshan Liu, Yan Liu, Xiaoyu Yu. Weight distributions of subfield codes from special functions[J]. AIMS Mathematics, 2026, 11(1): 2797-2815. doi: 10.3934/math.2026112
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