A Z8-linear lift of the binary Golay code and a nonlinear binary (96, 237, 24)-code

IM Duursma; M Greferath; SN Litsyn; SE Schmidt

doi:10.1109/18.923742

A Z8-linear lift of the binary Golay code and a nonlinear binary (96, 237, 24)-code

IM Duursma^*, M Greferath, SN Litsyn, SE Schmidt

^*Corresponding author for this work

Not published at Aalto University

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

7 Citations (Scopus)

Abstract

We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96, 2(36), 24) code as the image of a Z(8)-linear Hensel lift of the binary Golay code. The union of this code with a relevant coset yields a (96, 2(37), 24) code. The tables in [2], and [12] show that this rode and some of its shortenings are better than the best (non)linear binary codes known so far. For instance, the best earlier known code of length 96 and minimum distance 24 had 2(33) words.

Original language	English
Pages (from-to)	1596-1598
Number of pages	3
Journal	IEEE Transactions on Information Theory
Volume	47
Issue number	4
DOIs	https://doi.org/10.1109/18.923742
Publication status	Published - May 2001
MoE publication type	A1 Journal article-refereed

Keywords

binary Golay code
codes over rings
Gray isometry
Hensel lifting
homogeneous weight

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10.1109/18.923742

http://dx.doi.org/10.1109/18.923742

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title = "A Z8-linear lift of the binary Golay code and a nonlinear binary (96, 237, 24)-code",

abstract = "We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96, 2(36), 24) code as the image of a Z(8)-linear Hensel lift of the binary Golay code. The union of this code with a relevant coset yields a (96, 2(37), 24) code. The tables in [2], and [12] show that this rode and some of its shortenings are better than the best (non)linear binary codes known so far. For instance, the best earlier known code of length 96 and minimum distance 24 had 2(33) words.",

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AU - Litsyn, SN

AU - Schmidt, SE

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AB - We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96, 2(36), 24) code as the image of a Z(8)-linear Hensel lift of the binary Golay code. The union of this code with a relevant coset yields a (96, 2(37), 24) code. The tables in [2], and [12] show that this rode and some of its shortenings are better than the best (non)linear binary codes known so far. For instance, the best earlier known code of length 96 and minimum distance 24 had 2(33) words.

KW - binary Golay code

KW - codes over rings

KW - Gray isometry

KW - Hensel lifting

KW - homogeneous weight

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ER -

A Z8-linear lift of the binary Golay code and a nonlinear binary (96, 237, 24)-code

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Keywords

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