Expanders on Matrices Over a Finite Chain Ring, I

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.

Quantum codes over a class of finite chain ring

In this study, we introduce a new Gray map which preserves the orthogonality from the chain ring F2 [u] / (u) to F s 2 where F2 is the finite field with two elements. We also give a condition of the existence for cyclic codes of odd length containing its dual over the ring F2 [u] / (u) . By taking advantage of this Gray map and the structure of the ring, we obtain two classes of binary quantum ...

A Theorem on Matrices over a Commutative Ring

On the Hamming distance of linear codes over a finite chain ring

Let R be a finite chain ring (e.g. a Galois ring), K its residue field and C a linear code over R. We prove that d(C), the Hamming distance of C, is d((C : α)), where (C : α) is a submodule quotient, α is a certain element of R and denotes the canonical projection to K. These two codes also have the same set of minimal codeword supports. We explicitly construct a generator matrix/polynomial of ...

On the Codes over a Semilocal Finite Ring

In this paper, we study the structure of cyclic, quasi cyclic, constacyclic codes and their skew codes over the finite ring R. The Gray images of cyclic, quasi cyclic, skew cyclic, skew quasi cyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains its dual has been given. The parameters of quantum error corr...