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Determining the Generalized Hamming Weight Hierarchy of the Binary Projective Reed-Muller Code

Ramkumar, Vinayak and Vajha, Myna and Kumar, Vijay P (2018) Determining the Generalized Hamming Weight Hierarchy of the Binary Projective Reed-Muller Code. In: 2018 Twenty Fourth National Conference on Communications (NCC), FEB 25-28, 2018, Hyderabad, INDIA.

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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 C, identify for each dimension nu, the smallest size of the support of a subcode of 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 1] 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 in 2]. This results in a characterization of the GHW hierarchy of binary PRM codes.

Item Type: Conference Proceedings
Additional Information: 24th National Conference on Communications (NCC), Hyderabad, INDIA, FEB 25-28, 2018
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: Id for Latest eprints
Date Deposited: 20 Mar 2019 05:50
Last Modified: 20 Mar 2019 05:50
URI: http://eprints.iisc.ac.in/id/eprint/61974

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