A Recursive Construction for Projective Reed-Muller Codes

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 c...

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Veröffentlicht in:IEEE transactions on information theory 2024-12, Vol.70 (12), p.8511-8523
1. Verfasser: San-Jose, Rodrigo
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2024.3483998