Reed-Muller codes: Projections onto GF(4) and multilevel construction

Ofer Amrani; Yair Be'ery

doi:10.1109/18.945270

Reed-Muller codes: Projections onto GF(4) and multilevel construction

Ofer Amrani^*, Yair Be'ery

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Letter › peer-review

Abstract

A projection of binary Reed-Muller codes R(r, m) onto GF (4) ^m-2 is presented. For an R(r, m) code, this operation yields a linear quaternary code with the same length, dimension, and minimum distance as the Reed-Muller R(r-1, m-2) code. Based upon this projection, multilevel construction is given for R(r, m), where the constituent codes applied to the different levels are themselves the Reed-Muller codes R(r - 2, m - 2) and R(r, m - 2), as well as the aforementioned quaternary code. This construction of Reed-Muller codes is readily applicable for their efficient decoding.

Original language	English
Pages (from-to)	2560-2565
Number of pages	6
Journal	IEEE Transactions on Information Theory
Volume	47
Issue number	6
DOIs	https://doi.org/10.1109/18.945270
State	Published - Sep 2001

Keywords

Mapping
Multilevel
Multistage
Projection
Reed-Muller codes

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10.1109/18.945270

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title = "Reed-Muller codes: Projections onto GF(4) and multilevel construction",

abstract = "A projection of binary Reed-Muller codes R(r, m) onto GF (4) m-2 is presented. For an R(r, m) code, this operation yields a linear quaternary code with the same length, dimension, and minimum distance as the Reed-Muller R(r-1, m-2) code. Based upon this projection, multilevel construction is given for R(r, m), where the constituent codes applied to the different levels are themselves the Reed-Muller codes R(r - 2, m - 2) and R(r, m - 2), as well as the aforementioned quaternary code. This construction of Reed-Muller codes is readily applicable for their efficient decoding.",

keywords = "Mapping, Multilevel, Multistage, Projection, Reed-Muller codes",

author = "Ofer Amrani and Yair Be'ery",

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AU - Be'ery, Yair

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N2 - A projection of binary Reed-Muller codes R(r, m) onto GF (4) m-2 is presented. For an R(r, m) code, this operation yields a linear quaternary code with the same length, dimension, and minimum distance as the Reed-Muller R(r-1, m-2) code. Based upon this projection, multilevel construction is given for R(r, m), where the constituent codes applied to the different levels are themselves the Reed-Muller codes R(r - 2, m - 2) and R(r, m - 2), as well as the aforementioned quaternary code. This construction of Reed-Muller codes is readily applicable for their efficient decoding.

AB - A projection of binary Reed-Muller codes R(r, m) onto GF (4) m-2 is presented. For an R(r, m) code, this operation yields a linear quaternary code with the same length, dimension, and minimum distance as the Reed-Muller R(r-1, m-2) code. Based upon this projection, multilevel construction is given for R(r, m), where the constituent codes applied to the different levels are themselves the Reed-Muller codes R(r - 2, m - 2) and R(r, m - 2), as well as the aforementioned quaternary code. This construction of Reed-Muller codes is readily applicable for their efficient decoding.

KW - Mapping

KW - Multilevel

KW - Multistage

KW - Projection

KW - Reed-Muller codes

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Reed-Muller codes: Projections onto GF(4) and multilevel construction

Abstract

Keywords

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