Classification of some families of quaternary Reed-Muller codes

Jaume Pernas; Jaume Pujol; Mercè Villanueva

doi:10.1109/TIT.2011.2119465

Classification of some families of quaternary Reed-Muller codes

Jaume Pernas, Jaume Pujol, Mercè Villanueva

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

2 Citations (Scopus)

Abstract

Recently, new families of quaternary linear Reed-Muller codes have been introduced. They satisfy that, after the Gray map, the corresponding ℤ4-linear codes have the same parameters and properties as the codes of the binary linear Reed-Muller family. A structural invariant, the dimension of the kernel, for binary codes is used to classify completely these ℤ4-linear codes. The dimension of the kernel for these ℤ4-linear codes is established generalizing the known results about the dimension of the kernel for ℤ4-linear Hadamard and ℤ4-linear extended 1-perfect codes. © 2011 IEEE.

Original language	English
Article number	6006598
Pages (from-to)	6043-6051
Journal	IEEE Transactions on Information Theory
Volume	57
Issue number	9
DOIs	https://doi.org/10.1109/TIT.2011.2119465
Publication status	Published - 1 Sep 2011

Keywords

ℤ -linear codes 4
kernel
quaternary codes
Reed-Muller codes

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10.1109/TIT.2011.2119465

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abstract = "Recently, new families of quaternary linear Reed-Muller codes have been introduced. They satisfy that, after the Gray map, the corresponding ℤ4-linear codes have the same parameters and properties as the codes of the binary linear Reed-Muller family. A structural invariant, the dimension of the kernel, for binary codes is used to classify completely these ℤ4-linear codes. The dimension of the kernel for these ℤ4-linear codes is established generalizing the known results about the dimension of the kernel for ℤ4-linear Hadamard and ℤ4-linear extended 1-perfect codes. {\textcopyright} 2011 IEEE.",

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AU - Pujol, Jaume

AU - Villanueva, Mercè

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Y1 - 2011/9/1

N2 - Recently, new families of quaternary linear Reed-Muller codes have been introduced. They satisfy that, after the Gray map, the corresponding ℤ4-linear codes have the same parameters and properties as the codes of the binary linear Reed-Muller family. A structural invariant, the dimension of the kernel, for binary codes is used to classify completely these ℤ4-linear codes. The dimension of the kernel for these ℤ4-linear codes is established generalizing the known results about the dimension of the kernel for ℤ4-linear Hadamard and ℤ4-linear extended 1-perfect codes. © 2011 IEEE.

AB - Recently, new families of quaternary linear Reed-Muller codes have been introduced. They satisfy that, after the Gray map, the corresponding ℤ4-linear codes have the same parameters and properties as the codes of the binary linear Reed-Muller family. A structural invariant, the dimension of the kernel, for binary codes is used to classify completely these ℤ4-linear codes. The dimension of the kernel for these ℤ4-linear codes is established generalizing the known results about the dimension of the kernel for ℤ4-linear Hadamard and ℤ4-linear extended 1-perfect codes. © 2011 IEEE.

KW - ℤ -linear codes 4

KW - kernel

KW - quaternary codes

KW - Reed-Muller codes

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DO - 10.1109/TIT.2011.2119465

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EP - 6051

IS - 9

M1 - 6006598

ER -

Classification of some families of quaternary Reed-Muller codes

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Keywords

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