On the next-to-minimal weight of projective Reed–Muller codes

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Abstract

In this paper we present several values for the next-to-minimal weights of projective Reed–Muller codes. We work over Fq with q3 since in [3] we have determined the complete values for the next-to-minimal weights of binary projective Reed–Muller codes. As in [3] here we also find examples of codewords with next-to-minimal weight whose set of zeros is not in a hyperplane arrangement.

MSC

94B05
94B27
11T71
14G50

Keywords

Projective Reed–Muller codes
Next-to-minimal weights
Higher Hamming weights

Cited by (0)

1

Both authors were partially supported by grants from CNPq and FAPEMIG (proc. no. CEX-APQ-01645-16).