The complete weight hierarchy of every decreasing norm-trace code is determined by a footprint maximization, recovering the Hermitian hierarchy as a special case.
A recursive construction for projective Reed-Muller codes
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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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The weight hierarchy of decreasing norm-trace codes
The complete weight hierarchy of every decreasing norm-trace code is determined by a footprint maximization, recovering the Hermitian hierarchy as a special case.