A Combinatorial construction of the Gray map over Galois rings

Bahattin Yildiz

doi:10.1016/j.disc.2008.09.002

A Combinatorial construction of the Gray map over Galois rings

Bahattin Yildiz

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

6 Scopus citations

Abstract

In this correspondence, we will introduce a new combinatorial method for a coordinate-wise construction of the homogeneous-weight preserving Gray map for Galois rings by using elementary tools from Affine Geometries. Our construction differs in the methods used from the algebraic constructions done previously in [M. Greferath, S.E. Schmidt, Gray Isometries for finite chain rings and a nonlinear ternary (36, 3¹², 15) code, IEEE Trans. Inform. Theory 45 (1999) 2522-2524; S. Ling, J.T. Blackford, Z_{p k + 1}-linear codes, IEEE Trans. Inform. Theory 48 (2002) 2592-2605].

Original language	English (US)
Pages (from-to)	3408-3412
Number of pages	5
Journal	Discrete Mathematics
Volume	309
Issue number	10
DOIs	https://doi.org/10.1016/j.disc.2008.09.002
State	Published - May 28 2009
Externally published	Yes

Keywords

Affine Geometries
Affine Hyperplanes
Galois rings
Gray maps
Homogenous weights
Linear codes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2008.09.002

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title = "A Combinatorial construction of the Gray map over Galois rings",

abstract = "In this correspondence, we will introduce a new combinatorial method for a coordinate-wise construction of the homogeneous-weight preserving Gray map for Galois rings by using elementary tools from Affine Geometries. Our construction differs in the methods used from the algebraic constructions done previously in [M. Greferath, S.E. Schmidt, Gray Isometries for finite chain rings and a nonlinear ternary (36, 312, 15) code, IEEE Trans. Inform. Theory 45 (1999) 2522-2524; S. Ling, J.T. Blackford, Zp k + 1-linear codes, IEEE Trans. Inform. Theory 48 (2002) 2592-2605].",

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T1 - A Combinatorial construction of the Gray map over Galois rings

AU - Yildiz, Bahattin

PY - 2009/5/28

Y1 - 2009/5/28

N2 - In this correspondence, we will introduce a new combinatorial method for a coordinate-wise construction of the homogeneous-weight preserving Gray map for Galois rings by using elementary tools from Affine Geometries. Our construction differs in the methods used from the algebraic constructions done previously in [M. Greferath, S.E. Schmidt, Gray Isometries for finite chain rings and a nonlinear ternary (36, 312, 15) code, IEEE Trans. Inform. Theory 45 (1999) 2522-2524; S. Ling, J.T. Blackford, Zp k + 1-linear codes, IEEE Trans. Inform. Theory 48 (2002) 2592-2605].

AB - In this correspondence, we will introduce a new combinatorial method for a coordinate-wise construction of the homogeneous-weight preserving Gray map for Galois rings by using elementary tools from Affine Geometries. Our construction differs in the methods used from the algebraic constructions done previously in [M. Greferath, S.E. Schmidt, Gray Isometries for finite chain rings and a nonlinear ternary (36, 312, 15) code, IEEE Trans. Inform. Theory 45 (1999) 2522-2524; S. Ling, J.T. Blackford, Zp k + 1-linear codes, IEEE Trans. Inform. Theory 48 (2002) 2592-2605].

KW - Affine Geometries

KW - Affine Hyperplanes

KW - Galois rings

KW - Gray maps

KW - Homogenous weights

KW - Linear codes

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DO - 10.1016/j.disc.2008.09.002

M3 - Article

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EP - 3412

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 10

ER -

A Combinatorial construction of the Gray map over Galois rings

Abstract

Keywords

ASJC Scopus subject areas

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