Z2Z4Z8-Cyclic Codes

Some notes on the characterization of two dimensional skew cyclic codes

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

On Skew Cyclic Codes over a Finite Ring

In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

Cyclic Orbit Codes with the Normalizer of a Singer Subgroup

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

Good Quasi-Cyclic Codes Derived From Irreducible Cyclic Codes

As a generalization of cyclic codes, quasi-cyclic codes contain many good linear codes. Extensive search is made and lots of good quasi-cyclic codes are obtained from irreducible cyclic codes. A new binary [95, 13, 40] code which improves the lower bound on the minimum distance, is also constructed. Index Term — Codes and coding, linear codes, cyclic codes, idempotent, irreducible codes, quasi-...