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

Iwan M. Duursma; Marcus Greferath; Simon N. Litsyn; Stefan E. Schmidt

doi:10.1109/18.923742

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

Iwan M. Duursma, Marcus Greferath, Simon N. Litsyn, Stefan E. Schmidt

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

Abstract

We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96, 2³⁶, 24) code as the image of a Z₈-linear Hensel lift of the binary Golay code. The union of this code with a relevant coset yields a (96, 2³⁷, 24) code. The tables in 2, and 12 show that this code 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 2³³ words.

Original language	English (US)
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
State	Published - May 2001

Keywords

Binary Golay code
Codes over rings
Gray isometry
Hensel lifting
Homogeneous weight

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Online availability

10.1109/18.923742

Library availability

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Cite this

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abstract = "We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96, 236, 24) code as the image of a Z8-linear Hensel lift of the binary Golay code. The union of this code with a relevant coset yields a (96, 237, 24) code. The tables in 2, and 12 show that this code 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 233 words.",

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AU - Schmidt, Stefan E.

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AB - We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96, 236, 24) code as the image of a Z8-linear Hensel lift of the binary Golay code. The union of this code with a relevant coset yields a (96, 237, 24) code. The tables in 2, and 12 show that this code 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 233 words.

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