Cyclic subcodes of generalized Reed-Muller codes

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

doi:10.1109/ISIT.1997.613171

Cyclic subcodes of generalized Reed-Muller codes

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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 language	English (US)
Title of host publication	Proceedings - 1997 IEEE International Symposium on Information Theory, ISIT 1997
Pages	254
Number of pages	1
DOIs	https://doi.org/10.1109/ISIT.1997.613171
State	Published - 1997
Externally published	Yes
Event	1997 IEEE International Symposium on Information Theory, ISIT 1997 - Ulm, Germany Duration: Jun 29 1997 → Jul 4 1997

Publication series

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

Other

Other	1997 IEEE International Symposium on Information Theory, ISIT 1997
Country/Territory	Germany
City	Ulm
Period	6/29/97 → 7/4/97

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Online availability

10.1109/ISIT.1997.613171

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Moreno, O, Duursma, IM, Cherdieu, JP & Edouard, A 1997, Cyclic subcodes of generalized Reed-Muller codes. in Proceedings - 1997 IEEE International Symposium on Information Theory, ISIT 1997., 613171, IEEE International Symposium on Information Theory - Proceedings, pp. 254, 1997 IEEE International Symposium on Information Theory, ISIT 1997, Ulm, Germany, 6/29/97. https://doi.org/10.1109/ISIT.1997.613171

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title = "Cyclic subcodes of generalized Reed-Muller codes",

abstract = "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.",

author = "O. Moreno and Duursma, {I. M.} and Cherdieu, {J. P.} and A. Edouard",

year = "1997",

doi = "10.1109/ISIT.1997.613171",

language = "English (US)",

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T1 - Cyclic subcodes of generalized Reed-Muller codes

AU - Moreno, O.

AU - Duursma, I. M.

AU - Cherdieu, J. P.

AU - Edouard, A.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

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M3 - Conference contribution

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T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 254

BT - Proceedings - 1997 IEEE International Symposium on Information Theory, ISIT 1997

T2 - 1997 IEEE International Symposium on Information Theory, ISIT 1997

Y2 - 29 June 1997 through 4 July 1997

ER -

Cyclic subcodes of generalized Reed-Muller codes

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