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Generalization of the Number of Cyclic Codes Over Prime Field GF (43).

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Title: Generalization of the Number of Cyclic Codes Over Prime Field GF (43).
Authors: Njeru, Edward Mutwiri1 mutwiriedward5@gmail.com, Kinyanjui, Jeremiah Ndung'u1 jkinyanjui@kyu.ac.ke, Nyaluke, Wesley Kiprono2 nyalukekiprono1990@gmail.com, Mude, Lao Hussein3 husseinlao@gmail.com
Source: IAENG International Journal of Applied Mathematics. Jul2026, Vol. 56 Issue 7, p2496-2508. 13p.
Subjects: Cyclic codes, Finite fields, Linear codes, Coding theory, Factorization
Abstract: This paper presents a generalization of the number of cyclic codes over prime field GF(43). Cyclic codes form an important class of linear codes widely used in communication systems due to their algebraic structure and efficient implementation. While extensive studies have been conducted on cyclic codes over smaller prime fields such as GF(17), GF(19), GF(23), GF(31), and GF(37), limited attention has been given to higher prime fields such as GF(43). In this work, the enumeration of cyclic codes is developed through the factorization of wn -1 over GF(43). The number of cyclic codes is expressed as N = (43k+1)r, where r is the number of distinct irreducible factors determined using cyclotomic cosets. Illustrative examples and tabulated results are provided for various values of n. Furthermore, a comparative analysis with known results over other prime fields demonstrate that the proposed formulation follows a consistent algebraic pattern, thereby validating the generalization. The results contribute to the advancement of coding theory over higher prime fields. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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: Generalization of the Number of Cyclic Codes Over Prime Field GF (43).
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  Data: <searchLink fieldCode="AR" term="%22Njeru%2C+Edward+Mutwiri%22">Njeru, Edward Mutwiri</searchLink><relatesTo>1</relatesTo><i> mutwiriedward5@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Kinyanjui%2C+Jeremiah+Ndung'u%22">Kinyanjui, Jeremiah Ndung'u</searchLink><relatesTo>1</relatesTo><i> jkinyanjui@kyu.ac.ke</i><br /><searchLink fieldCode="AR" term="%22Nyaluke%2C+Wesley+Kiprono%22">Nyaluke, Wesley Kiprono</searchLink><relatesTo>2</relatesTo><i> nyalukekiprono1990@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Mude%2C+Lao+Hussein%22">Mude, Lao Hussein</searchLink><relatesTo>3</relatesTo><i> husseinlao@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jul2026, Vol. 56 Issue 7, p2496-2508. 13p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Cyclic+codes%22">Cyclic codes</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+fields%22">Finite fields</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+codes%22">Linear codes</searchLink><br /><searchLink fieldCode="DE" term="%22Coding+theory%22">Coding theory</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper presents a generalization of the number of cyclic codes over prime field GF(43). Cyclic codes form an important class of linear codes widely used in communication systems due to their algebraic structure and efficient implementation. While extensive studies have been conducted on cyclic codes over smaller prime fields such as GF(17), GF(19), GF(23), GF(31), and GF(37), limited attention has been given to higher prime fields such as GF(43). In this work, the enumeration of cyclic codes is developed through the factorization of wn -1 over GF(43). The number of cyclic codes is expressed as N = (43k+1)r, where r is the number of distinct irreducible factors determined using cyclotomic cosets. Illustrative examples and tabulated results are provided for various values of n. Furthermore, a comparative analysis with known results over other prime fields demonstrate that the proposed formulation follows a consistent algebraic pattern, thereby validating the generalization. The results contribute to the advancement of coding theory over higher prime fields. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 2496
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      – SubjectFull: Cyclic codes
        Type: general
      – SubjectFull: Finite fields
        Type: general
      – SubjectFull: Linear codes
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      – SubjectFull: Coding theory
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      – SubjectFull: Factorization
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              M: 07
              Text: Jul2026
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              Y: 2026
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