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On codes over product of finite chain rings.

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Title: On codes over product of finite chain rings.
Authors: BAJALAN, Maryam1, REZAEI, Rashid1 ras_rezaei@yahoo.com, SAMEI, Karim2
Source: Sigma: Journal of Engineering & Natural Sciences / Mühendislik ve Fen Bilimleri Dergisi. Feb2023, Vol. 41 Issue 1, p145-155. 11p.
Subjects: Finite rings, Product coding, Parity-check matrix, Finite fields
Abstract: In this paper, codes over the direct product of two finite commutative chain rings are studied. The standard form of the parity-check matrix is determined. The structure of self-dual codes is described. A distance preserving Gray map from the direct product of chain rings to a finite field is defined. Two upper bounds on minimum distance are obtained. [ABSTRACT FROM AUTHOR]
Copyright of Sigma: Journal of Engineering & Natural Sciences / Mühendislik ve Fen Bilimleri Dergisi is the property of Sigma: Journal of Engineering & Natural Sciences / Mühendislik ve Fen Bilimleri Dergisi and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: On codes over product of finite chain rings.
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  Data: <searchLink fieldCode="DE" term="%22Finite+rings%22">Finite rings</searchLink><br /><searchLink fieldCode="DE" term="%22Product+coding%22">Product coding</searchLink><br /><searchLink fieldCode="DE" term="%22Parity-check+matrix%22">Parity-check matrix</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+fields%22">Finite fields</searchLink>
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  Data: In this paper, codes over the direct product of two finite commutative chain rings are studied. The standard form of the parity-check matrix is determined. The structure of self-dual codes is described. A distance preserving Gray map from the direct product of chain rings to a finite field is defined. Two upper bounds on minimum distance are obtained. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Sigma: Journal of Engineering & Natural Sciences / Mühendislik ve Fen Bilimleri Dergisi is the property of Sigma: Journal of Engineering & Natural Sciences / Mühendislik ve Fen Bilimleri Dergisi and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.14744/sigma.2023.00014
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      – Code: eng
        Text: English
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        PageCount: 11
        StartPage: 145
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      – SubjectFull: Finite rings
        Type: general
      – SubjectFull: Product coding
        Type: general
      – SubjectFull: Parity-check matrix
        Type: general
      – SubjectFull: Finite fields
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      – TitleFull: On codes over product of finite chain rings.
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            NameFull: BAJALAN, Maryam
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            NameFull: REZAEI, Rashid
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            NameFull: SAMEI, Karim
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              Text: Feb2023
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              Y: 2023
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              Value: 41
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            – TitleFull: Sigma: Journal of Engineering & Natural Sciences / Mühendislik ve Fen Bilimleri Dergisi
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