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Construction of a Class of Real Array Rank Distance Codes.

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Title: Construction of a Class of Real Array Rank Distance Codes.
Authors: Babu, N. Suresh1 (AUTHOR), Ravivarma, B.1 (AUTHOR), Elsayed, E. M.2,3 (AUTHOR), Sreekumar, K. G.4 (AUTHOR)
Source: Journal of Electrical & Computer Engineering. 10/28/2023, p1-9. 9p.
Subjects: Space-time codes, Finite fields, Linear network coding, Linear codes, Data warehousing, Rating of students
Abstract: Rank distance codes are known to be applicable in various applications such as distributed data storage, cryptography, space time coding, and mainly in network coding. Rank distance codes defined over finite fields have attracted considerable attention in recent years. However, in some scenarios where codes over finite fields are not sufficient, it is demonstrated that codes defined over the real number field are preferred. In this paper, we proposed a new class of rank distance codes over the real number field R. The real array rank distance (RARD) codes we constructed here can be used for all the applications mentioned above whenever the code alphabet is the real field R. From the class of RARD codes, we extract a subclass of equidistant constant rank codes which is applicable in network coding. Also, we determined an upper bound for the dimension of RARD codes leading the way to obtain some optimal RARD codes. Moreover, we established examples of some RARD codes and optimal RARD codes. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Electrical & Computer Engineering is the property of Wiley-Blackwell 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.)
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  Data: Construction of a Class of Real Array Rank Distance Codes.
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  Label: Abstract
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  Data: Rank distance codes are known to be applicable in various applications such as distributed data storage, cryptography, space time coding, and mainly in network coding. Rank distance codes defined over finite fields have attracted considerable attention in recent years. However, in some scenarios where codes over finite fields are not sufficient, it is demonstrated that codes defined over the real number field are preferred. In this paper, we proposed a new class of rank distance codes over the real number field R. The real array rank distance (RARD) codes we constructed here can be used for all the applications mentioned above whenever the code alphabet is the real field R. From the class of RARD codes, we extract a subclass of equidistant constant rank codes which is applicable in network coding. Also, we determined an upper bound for the dimension of RARD codes leading the way to obtain some optimal RARD codes. Moreover, we established examples of some RARD codes and optimal RARD codes. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Electrical & Computer Engineering is the property of Wiley-Blackwell 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: 10.1155/2023/9952813
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      – Code: eng
        Text: English
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        PageCount: 9
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      – SubjectFull: Finite fields
        Type: general
      – SubjectFull: Linear network coding
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      – SubjectFull: Linear codes
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      – SubjectFull: Data warehousing
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      – SubjectFull: Rating of students
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      – TitleFull: Construction of a Class of Real Array Rank Distance Codes.
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            – D: 28
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              Text: 10/28/2023
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              Y: 2023
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