Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, [37] constructed a class of cyclic codes with arbitrary number of zeros, and computed the weight distributions for several cases. In this paper, we determine the weight distribution ...

Because of efficient encoding and decoding algorithms, cyclic codes are an important family of linear block codes, and have applications in communication and storage systems. However, their weight distributions are known only for a few cases mainly on the codes with one or two nonzeros. In this paper, the weight distributions of two classes of cyclic codes with three or four nonzeros are determ...

The purpose of this paper is to study the cyclic self orthogonal codes over Zpm . After providing the generator polynomial of cyclic self orthogonal codes over Zpm , we give the necessary and sufficient condition for the existence of non-trivial self orthogonal codes over Zpm . We have also provided the number of such codes of length n over Zpm for any (p, n) = 1.

A new Gray map which is both an isometry and a weight preserving map from R = F2 + vF2 + v 2F2 to F 3 2 is defined. A construction for quantum error correcting codes from cyclic codes over finite ring R = F2 + vF2 + v 2F2, v 3 = v is given.The parameters of quantum codes which are obtained from cyclic codes over R are determined.

Linear complementary dual (LCD) codes play an important role in data storage, communications systems and cryptography. In this paper, we construct some symplectic LCD from quasi-cyclic (QC) codes, prove that these with dimension two over \begin{document}$ \mathbb{F}_{2^a} $\end{document} are maximum-dista...

Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting information from decoherence and noise. In this work, we construct six families of new EAQECCs lengths $$n=(q^2+1)/a$$ , $$n=q^2+1$$ $$n=(q^2+1)/2$$ cyclic codes, where $$a=m^2+1$$ ( $$m\ge 1$$ is odd) q an odd prime power with the form $$a|(q+m)$$ or $$a|(q-m)$$ . Moreover, those are entangleme...

The paper has a threefold purpose. The first purpose is to present an explicit description of expanded cyclic codes defined in GF(qm). The proposed explicit construction of expanded generator matrix and expanded parity check matrix maintains the symbol-wise algebraic structure and thus keeps many important original characteristics. The second purpose of this paper is to identify a class of cons...

We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form p = 4n ± 1. The proposed Type-I stabilizer codes are of cyclic structure and code length N = p. They are constructed based on multi-weight circulant matrix generated from idempotent polynomial, which is obtained from a quadratic residue set. The proposed Type...