The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this work, we propose a decomposition of the defining set of constacyclic codes. Using this method, we construct four classes of q-ary entanglement-assisted quant...

Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair costs by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs been widely investigated. Optimal via cyclic constacyclic provide significant benefits elegant algebraic structure efficient encoding procedure. In this paper, ...

In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes. And we give some results on Hermitian self-dual codes, which are the extended cyclic duadic codes.

For λ an n-th power of a unit in a finite chain ring we prove that λ-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the α+pβconstacyclic codes of length p over the Galois ring GR(p, r).

We present two families of constacyclic linear codes with large automorphism groups. The codes are obtained from the twisted tensor product construction. AMS subject classification: 05E20, 05B25, 11T71, 94B25, 94B27, 51E22, 51E20, 20G40, 14L35

For any prime number p, positive integers m, k, n satisfying gcd(p, n) = 1 and λ0 ∈ F × pm, we prove that any λ p 0 -constacyclic code of length p n over the finite field Fpm is monomially equivalent to a matrix-product code of a nested sequence of p λ0-constacyclic codes with length n over Fpm.