Composition of Gray Isometries

Composition of Gray Isometries

In classical coding theory, Gray isometries are usually defined as mappings between finite Frobenius rings, which include the ring \(Z_m\) of integers modulo \(m\), and the finite fields. In this paper, we derive an isometric mapping from \(Z_8\) to \(Z_4^2\) from the composition of the Gray isometr...

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Veröffentlicht in:arXiv.org 2017-06
Hauptverfasser: Sierra Marie M Lauresta, Sison, Virgilio P
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Block codes
Composition
Fields (mathematics)
Integers
Mapping
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description In classical coding theory, Gray isometries are usually defined as mappings between finite Frobenius rings, which include the ring \(Z_m\) of integers modulo \(m\), and the finite fields. In this paper, we derive an isometric mapping from \(Z_8\) to \(Z_4^2\) from the composition of the Gray isometries on \(Z_8\) and on \(Z_4^2\). The image under this composition of a \(Z_8\)-linear block code of length \(n\) with homogeneous distance \(d\) is a (not necessarily linear) quaternary block code of length \(2n\) with Lee distance \(d\).
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subjects Block codes
Composition
Fields (mathematics)
Integers
Mapping
title Composition of Gray Isometries
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