On the covering radius of first order generalized Reed-Muller codes
Elodie Leducq
TL;DR
This paper extends known theorems on the covering radius of linear codes to any q, determines the covering radius of first order generalized Reed-Muller codes within second order codes, and provides bounds with computational improvements for q=3.
Contribution
It generalizes a theorem to all q and precisely determines the covering radius of certain Reed-Muller codes, offering new bounds and computational enhancements.
Findings
Determined the covering radius of first order generalized Reed-Muller codes in second order codes.
Provided bounds for the covering radius of these codes.
Achieved computational improvements for q=3 using Magma.
Abstract
We generalize to any q a theorem about covering radius of linear codes proved by Helleseth, Klove and Mykkelvit. Then we determine the covering radius of first order generalized Reed-Muller codes in second order generalized Reed-Muller codes. Using these results, we are able to give bounds for the covering radius of first order generalized Reed-Muller codes. Finaly, using Magma, we get some improvements for q=3.
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Taxonomy
TopicsCoding theory and cryptography · Error Correcting Code Techniques · DNA and Biological Computing