Cyclic subcodes of generalized Reed-Muller codes

O. Moreno, I. M. Duursma, J. P. Cherdieu, A. Edouard

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We define homogeneous generalised Reed-Muller codes (HRM codes). These are subcodes of the generalized Reed-Muller (GRM) codes. We show, that while they have less information symbols, there is a significant increase in the minimum distance. HRM codes are also naturally related to projective Reed-Muller codes (PRM codes). In particular, we can deduce their parameters from the PRM codes. We show, that punctured HRM codes are cyclic, while PRM codes in general are not. Hence, HRM codes compare favorably to both GRM codes and PRM codes. We show that binary trace codes of q-ary HRM codes are well-defined and give their parameters. The trace codes include codes that have the same length and minimum distance as some classical RM codes, but with a significant increase in the dimension.

Original languageEnglish (US)
Title of host publicationProceedings - 1997 IEEE International Symposium on Information Theory, ISIT 1997
Number of pages1
StatePublished - 1997
Externally publishedYes
Event1997 IEEE International Symposium on Information Theory, ISIT 1997 - Ulm, Germany
Duration: Jun 29 1997Jul 4 1997

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Other1997 IEEE International Symposium on Information Theory, ISIT 1997

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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