In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct codes in context function fields over a finite field by using their group automorphisms. prove that constructed way are closely related extensions. also detailed monomial equivalence with our method case rational field.

Cyclic codes are very useful in error correcting codes. Hence, the construction of good cyclic codes is of utmost importance. A generic class of polynomials called generator polynomials is used to construct the cyclic codes. Finding a generator polynomial necessitates factoring a base polynomial called monic polynomial. Unfortunately, factoring a polynomial is not always an easy task. Idempoten...

We give an algorithm for generating cyclic self-orthogonal (CSO) codes for an arbitrary positive integer n with gcd(n; q) = 1. Given a cyclic q-ary code of length n, we determine how many codes isomorphic to the given code are cyclic. We introduce a mass formula for CSO(n; q) codes of maximum dimension. Using the mass formula we classify CSO(63; 2) codes. This mass formula works for any cyclic ...

A binary linear code C is a Z2-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the Z2[x]-module Z2[x]/(x r −1)×Z2[x]/(x − 1). We determine the structure of Z2-double cyclic codes giving the generator polynomials of these codes. ...

Symbol-pair codes are proposed to protect against pair-errors in symbol-pair read channels. The research of with the largest possible minimum distance is great significance since such have best error-correcting capability. A code meeting Singleton bound called a maximum separable (MDS) code. In this paper, two new classes MDS by utilizing repeated-root cyclic over finite fields odd characterist...

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over finite fields with even characteristic are employed to construct a number of families of binary cyclic codes. Lower bounds on the minimum weight of some fam...

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear functions and planar functions over finite fields are employed to construct a number of classes of cyclic codes. Lower bounds on the minimum weight of some class...

Duadic codes were introduced by Leon et al. [5] as cyclic codes generalizing quadratic residue codes. Brualdi and Pless generalized them to polyadic cyclic codes [2] and Rushanan did so to duadic Abelian group codes [9]. Theorems concerning the existence of these codes in terms of field and group restrictions have been proved during this development, beginning with the one of Smid for cyclic du...