Abstract
This paper is devoted to the affine-invariant ternary codes defined by Hermitian functions. We first compute the incidence matrices of the 2-designs supported by the minimum weight codewords of these ternary codes. Then we show that the linear codes spanned by the rows of these incidence matrices are subcodes of the 4-th order generalized Reed-Muller codes and also hold 2-designs. Finally, we determine the dimension and develop a lower bound on the minimum distance of the ternary linear codes.
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Acknowledgments
The work of the first author was supported by The National Natural Science Foundation of China under Grant No. 11771392.
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National Natural Science Foundation of China under Grant No. 11771392.
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He, Z., Wen, J. Linear codes of 2-designs as subcodes of the generalized Reed-Muller codes. Cryptogr. Commun. 13, 407–423 (2021). https://doi.org/10.1007/s12095-021-00472-4
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DOI: https://doi.org/10.1007/s12095-021-00472-4