Construction of ℤ4-Linear Reed-Muller codes

Jaume Pujol; Josep Rifa; Fiana Ivanovna Solov'eva

doi:10.1109/TIT.2008.2008143

Construction of ℤ₄-Linear Reed-Muller codes

Jaume Pujol^*, Josep Rifa, Fiana Ivanovna Solov'eva

^*Autor corresponent d’aquest treball

Departament d'Enginyeria de la Informació i de les Comunicacions

Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

16 Cites (Scopus)

Resum

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.

Idioma original	Anglès
Pàgines (de-a)	99-104
Nombre de pàgines	6
Revista	IEEE Transactions on Information Theory
Volum	55
Número	1
DOIs	https://doi.org/10.1109/TIT.2008.2008143
Estat de la publicació	Publicada - 2009

Accés al document

10.1109/TIT.2008.2008143

Altres arxius i enllaços

Link to publication in Scopus

Com citar-ho

@article{65dca3fe638849d8bc43b9fa8e360063,

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.",

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

author = "Jaume Pujol and Josep Rifa and Solov'eva, {Fiana Ivanovna}",

note = "Funding Information: Manuscript received January 19, 2008; revised July 03, 2008. Current version published December 24, 2008. This work was supported in part by the Spanish MEC Grants MTM2006-03250, TSI2006-14005-C02-01, and PCI2006-A7-0616. The material in this paper was presented in part at the 17th Symposium on Applied Algebra, Algebraic Algorithms, and Error Correcting Codes, Bangalore, India, December 2007.",

year = "2009",

doi = "10.1109/TIT.2008.2008143",

language = "English",

volume = "55",

pages = "99--104",

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TY - JOUR

T1 - Construction of ℤ4-Linear Reed-Muller codes

AU - Pujol, Jaume

AU - Rifa, Josep

AU - Solov'eva, Fiana Ivanovna

N1 - Funding Information: Manuscript received January 19, 2008; revised July 03, 2008. Current version published December 24, 2008. This work was supported in part by the Spanish MEC Grants MTM2006-03250, TSI2006-14005-C02-01, and PCI2006-A7-0616. The material in this paper was presented in part at the 17th Symposium on Applied Algebra, Algebraic Algorithms, and Error Correcting Codes, Bangalore, India, December 2007.

PY - 2009

Y1 - 2009

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.

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.

KW - ℤ-linear codes

KW - Additive codes

KW - Kronecker inner product

KW - Plotkin construction

KW - Quaternary codes

KW - Reed-Muller (RM) codes

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U2 - 10.1109/TIT.2008.2008143

DO - 10.1109/TIT.2008.2008143

M3 - Article

AN - SCOPUS:58249125451

SN - 0018-9448

VL - 55

SP - 99

EP - 104

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 1