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]
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Database:	Engineering Source

Description
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]
ISSN:	19929978