A recursive construction for projective Reed-Muller codes

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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Cited by in corpus (2)

• Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem
• About the generalized Hamming weights of matrix-product codes