Construction of ℤ<inf>4</inf>-Linear Reed-Muller codes

Jaume Pujol; Josep Rifa; Fiana Ivanovna Solov'eva

doi:https://doi.org/10.1109/TIT.2008.2008143

Construction of ℤ<inf>4</inf>-Linear Reed-Muller codes

Jaume Pujol, Josep Rifa, Fiana Ivanovna Solov'eva

Department of Information and Communications Engineering

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

13 Citations (Scopus)

Abstract

In this paper, new quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension, and the minimum distance, are studied. Using these constructions, new families of quaternary Reed-Muller (RM) codes are built with the peculiarity that after using the Gray map the obtained ℤ4-linear codes have the same parameters and fundamental properties as the codes in the usual binary linear RM family. To make the duality relationships in the constructed families more evident, the concept of Kronecker inner product is introduced. © 2009 IEEE.

Original language	English
Pages (from-to)	99-104
Journal	IEEE Transactions on Information Theory
Volume	55
DOIs	https://doi.org/10.1109/TIT.2008.2008143
Publication status	Published - 22 Jan 2009

Keywords

Additive codes
Kronecker inner product
Plotkin construction
Quaternary codes
Reed-Muller (RM) codes
ℤ -linear codes 4

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title = "Construction of ℤ4-Linear Reed-Muller codes",

abstract = "In this paper, new quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension, and the minimum distance, are studied. Using these constructions, new families of quaternary Reed-Muller (RM) codes are built with the peculiarity that after using the Gray map the obtained ℤ4-linear codes have the same parameters and fundamental properties as the codes in the usual binary linear RM family. To make the duality relationships in the constructed families more evident, the concept of Kronecker inner product is introduced. {\textcopyright} 2009 IEEE.",

keywords = "Additive codes, Kronecker inner product, Plotkin construction, Quaternary codes, Reed-Muller (RM) codes, ℤ -linear codes 4",

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AU - Pujol, Jaume

AU - Rifa, Josep

AU - Solov'eva, Fiana Ivanovna

PY - 2009/1/22

Y1 - 2009/1/22

N2 - In this paper, new quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension, and the minimum distance, are studied. Using these constructions, new families of quaternary Reed-Muller (RM) codes are built with the peculiarity that after using the Gray map the obtained ℤ4-linear codes have the same parameters and fundamental properties as the codes in the usual binary linear RM family. To make the duality relationships in the constructed families more evident, the concept of Kronecker inner product is introduced. © 2009 IEEE.

AB - In this paper, new quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension, and the minimum distance, are studied. Using these constructions, new families of quaternary Reed-Muller (RM) codes are built with the peculiarity that after using the Gray map the obtained ℤ4-linear codes have the same parameters and fundamental properties as the codes in the usual binary linear RM family. To make the duality relationships in the constructed families more evident, the concept of Kronecker inner product is introduced. © 2009 IEEE.

KW - Additive codes

KW - Kronecker inner product

KW - Plotkin construction

KW - Quaternary codes

KW - Reed-Muller (RM) codes

KW - ℤ -linear codes 4

U2 - https://doi.org/10.1109/TIT.2008.2008143

DO - https://doi.org/10.1109/TIT.2008.2008143

M3 - Article

VL - 55

SP - 99

EP - 104

ER -

Construction of ℤ<inf>4</inf>-Linear Reed-Muller codes

Abstract

Keywords

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