A recursive construction for projective Reed-Muller codes

Author:

Rodrigo San-José

Keyword:

Computer Science, Information Theory, Information Theory (cs.IT), Commutative Algebra (math.AC)

journal:

date:

2023-12-08 00:00:00

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 are able to derive a lower bound for the generalized Hamming weights of projective Reed-Muller codes which, together with the basic properties of the generalized Hamming weights, allows us to determine most of the weight hierarchy of projective Reed-Muller codes in many cases.

PDF: A recursive construction for projective Reed-Muller codes.pdf