On the covering radius of first order generalized Reed-Muller codes

2011/02/10 by Leducq, Elodie · 2 citations
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1102.2122

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.

Cited by

• The covering radius of Butson Hadamard codes for the homogeneous metric
• On irredundant orthogonal arrays

Related

• The Covering Radius of the Reed--Muller Code RM(2,7) is 40
• On the Covering Radius of the Second Order Reed-Muller Code of Length 128
• On the Generalized Covering Radii of Reed-Muller Codes
• A Generalized Covering Algorithm for Chained Codes
• The Covering Radius of the Reed-Muller Code RM(m-4,m) in RM(m-3,m)