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- W4302183851 abstract "Projective Reed-Muller codes correspond to subcodes of the Reed-Muller code in which the polynomials being evaluated to yield codewords, are restricted to be homogeneous. The Generalized Hamming Weights (GHW) of a code ${cal C}$, identify for each dimension $nu$, the smallest size of the support of a subcode of ${cal C}$ of dimension $nu$. The GHW of a code are of interest in assessing the vulnerability of a code in a wiretap channel setting. It is also of use in bounding the state complexity of the trellis representation of the code. In prior work by the same authors, a code-shortening algorithm was employed to derive upper bounds on the GHW of binary projective, Reed-Muller (PRM) codes. In the present paper, we derive a matching lower bound by adapting the proof techniques used originally for Reed-Muller (RM) codes by Wei. This results in a characterization of the GHW hierarchy of binary PRM codes." @default.
- W4302183851 created "2022-10-06" @default.
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- W4302183851 date "2018-06-06" @default.
- W4302183851 modified "2023-09-30" @default.
- W4302183851 title "Determining the Generalized Hamming Weight Hierarchy of the Binary Projective Reed-Muller Code" @default.
- W4302183851 doi "https://doi.org/10.48550/arxiv.1806.02028" @default.
- W4302183851 hasPublicationYear "2018" @default.
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