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arXiv · 2312.05072

A recursive construction for projective Reed-Muller codes

Rodrigo San-José
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Abstract

We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of projective Reed-Muller codes for some particular degrees that give codes with good parameters. Moreover, from this recursive construction we derive a lower bound for the generalized Hamming weights of projective Reed-Muller codes which is sharp in most of the cases we have checked.

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Rodrigo San-José. 2023-12-08. A recursive construction for projective Reed-Muller codes. https://doi.org/10.1109/tit.2024.3483998

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