The Permutation Groups and the Equivalence of Cyclic and Quasi-Cyclic Codes

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

On the Automorphism Groups and Equivalence of Cyclic Combinatorial Objects

We determine the permutation groups that arise as the automorphism groups of cyclic combinatorial objects. As special cases we classify the automorphism groups of cyclic codes. We also give the permutations by which two cyclic combinatorial objects on p elements are equivalent.

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...

Equivalence of Quasi-cyclic Codes over Finite Fields

This paper considers the equivalence problem for quasi-cyclic codes over finite fields. The results obtained are used to construct isodual quasi-cyclic codes.

The q-ary image of some qm-ary cyclic codes: Permutation group and soft-decision decoding

Using a particular construction of generator matrices of the -ary image of -ary cyclic codes, it is proved that some of these codes are invariant under the action of particular permutation groups. The equivalence of such codes with some two-dimensional (2-D) Abelian codes and cyclic codes is deduced from this property. These permutations are also used in the area of the soft-decision decoding o...