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Gray map; -linear code; -additive code; Kernel; Rank; Classification application/pdf https://doi.org/10.1007/s10623-025-01696-8 Springer US Designs, Codes and Cryptography, https://doi.org/10.1007/s10623-025-01696-8 Hadamard code Gray map -linear code -additive code Kernel Rank Classification Linearity and classification of -linear Hadamard codes Dipak K. 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