Abstract
Using Plücker coordinates we construct a matrix whose columns parametrize all projective isotropic lines in a symplectic space E of dimension 4 over a finite field \(\mathbb{F}_{q}\). As an application of this construction we explicitly obtain the smallest subfamily of algebro-geometric codes defined by the corresponding Lagrangian-Grassmannian variety. Furthermore, we show that this subfamily is a class of three-weight linear codes over \(\mathbb{F}_{q}\) of length (q 4 − 1)/(q − 1), dimension 5, and minimum Hamming distance q 3 − q.
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Carrillo-Pacheco, J., Vega, G., Zaldívar, F. (2015). The Weight Distribution of a Family of Lagrangian-Grassmannian Codes. In: El Hajji, S., Nitaj, A., Carlet, C., Souidi, E. (eds) Codes, Cryptology, and Information Security. C2SI 2015. Lecture Notes in Computer Science(), vol 9084. Springer, Cham. https://doi.org/10.1007/978-3-319-18681-8_19
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DOI: https://doi.org/10.1007/978-3-319-18681-8_19
Publisher Name: Springer, Cham
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