Cyclic Codes from a Sequence over Finite Fields

A cyclic code has been one of the most active research topics in coding theory because they have many applications in data storage systems and communication systems. They have efficient encoding and decoding algorithms. This paper explains the construction of a family of cyclic codes from sequences generated by a trace of a monomial over finite fields of odd characteristics. The parameter and some examples of the codes are presented in this paper.

On skew cyclic codes over a mixed alphabet and their applications to DNA codes

In this paper, we introduce skew cyclic codes over the mixed alphabet [Formula: see text], where [Formula: see text] is the finite field with 4 elements and [Formula: see text]. Our results include a description of the generator polynomials of such codes and a necessary and sufficient condition for an [Formula: see text]-skew cyclic code to be reversible complement.

KODE SIKLIK BERULANG DARI KODE LINEAR F_p ATAS LAPANGAN HINGGA F_(p^l ) DENGAN l BILANGAN PRIMA TERTENTU

Kode blok adalah skema penyandian yang menggunakan sistem kode-kode pada suatu lapangan hingga dengan panjang yang sama dan tetap. Kode blok linear atau lebih sering disebut kode linear atas suatu lapangan hingga merupakan himpunan kode-kode blok dengan panjang yang membentuk suatu subruang bagian atas lapangan hingga dengan adalah bilangan prima dan bilangan bulat positif. Sedangkan kode linear dikatakan kode siklik jika setiap elemennya diputar masih terdapat di himpunan kode linear . Setiap kode blok di kode siklik mempunyai korespondensi dengan semua faktorisasi polinomial tak tereduksi dari polinmial . Umumnya, pembahasan mengenai kode siklik pada lapangan hingga hanya dibatasi oleh Hal ini menyebabkan setiap faktor dari polinomial adalah tunggal. Untuk , memunculkan suatu pendefinisian baru dari konsep kode siklik. Kode siklik ini disebut disebut kode siklik berulang (repeated cyclic code). Penelitian ini mencakup sifat dan struktur ring dari kode linear atas ring rangkaian komutatif hingga, kontruksi kode siklik berulang, algoritma dari kontruksi kode siklik atas lapangan hingga dengan bilangan prima tertentu.

Triple Cyclic Codes Over 𝔽q + u𝔽q

Let [Formula: see text], where [Formula: see text] is a power of a prime number [Formula: see text] and [Formula: see text]. A triple cyclic code of length [Formula: see text] over [Formula: see text] is a set that can be partitioned into three parts that any cyclic shift of the coordinates of the three parts leaves the code invariant. These codes can be viewed as [Formula: see text]-submodules of [Formula: see text]. In this paper, we study the generator polynomials and the minimum generating sets of this kind of codes. Some optimal or almost optimal linear codes are obtained from this family of codes. We present the relationship between the generators of triple cyclic codes and their duals. As a special class of triple cyclic codes, separable codes over [Formula: see text] are discussed briefly in the end.

A Note on Skew Cyclic Codes over a Class of Rings

We study skew cyclic codes over a class of rings [Formula: see text], where each [Formula: see text] [Formula: see text] is a finite field. We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R. Moreover, we discuss possible extension of our results in the more general setting of [Formula: see text]-dual skew constacyclic codes over R, where δR is an automorphism of R.

Abelian group factorization from cyclic and quasi-cyclic codes

In this paper, we use the algebraic structures of cyclic codes and algorithmic techniques to find factorizations of abelian groups from cyclic codes. We construct specific subclasses of quasi-cyclic codes and provide the conditions with which we obtain a normalized factorization of certain abelian groups. The factorization, in both cases, is constituted by two sets, one corresponding to the cyclic code and the other corresponding to the words that represent all possible error polynomials of the cyclic code besides the zero vector.