Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algorithm for factorizing xn − λ over Fq2 is given, where λ is a unit in Fq2 . Based on this factorization, the dimensions of the Hermitian hulls of λ-constacyclic codes of length n over Fq2 are determined. The characterization and enumeration of constacyclic Hermitian self-dual (resp., complementary dua...

Generalizing Euclidean inner product and Hermitian inner product, we introduce Galois inner products, and study the Galois self-dual constacyclic codes in a very general setting by a uniform method. The conditions for existence of Galois self-dual and isometrically Galois self-dual constacyclic codes are obtained. As consequences, the results on self-dual, iso-dual and Hermitian self-dual const...

In this paper, we study constacyclic codes over Fp+vFp, where p is an odd prime and v = v. The polynomial generators of all constacyclic codes over Fp + vFp are characterized and their dual codes are also determined.

We introduce a Gray map from F2m + uF2m to F 2m 2 and study (1 + u)-constacyclic codes over F2m + uF2m ,where u 2 = 0. It is proved that the image of a (1+u)-constacyclic code length n overF2m+uF2m under the Gray map is a distance-invariant quasi-cyclic code of indexm and length 2mn over F2. We also prove that every code of length 2mnwhich is the Gray image of cyclic codes overF2m+uF2m of lengt...

The results of J. F. Qian et al. [5] on (1 − γ)-constacyclic codes over finite chain rings of nilpotency index 2 are extended to (1 − γe)constacyclic codes over finite chain rings of arbitrary nilpotency index e+1. The Gray map is introduced for this type of rings. We prove that the Gray image of a linear (1− γe)-constacyclic code over a finite chain ring is a distance-invariant quasi-cyclic co...

For any prime p, λ-constacyclic codes of length p over R = Fpm + uFpm are precisely the ideals of the local ring Rλ = R[x] 〈xp−λ〉 , where u = 0. In this paper, we first investigate the Hamming distances of cyclic codes of length p over R. The minimum Hamming distances of all cyclic codes of length p over R are determined. Moreover, an isometry between cyclic and α-constacyclic codes of length p...

We first define a new Gray map from R = Z4+uZ4 to Z 2 4, where u 2 = 1 and study (1 + 2u)-constacyclic codes over R. Also of interest are some properties of (1 + 2u)constacyclic codes over R. Considering their Z4 images, we prove that the Gray images of (1+2u)-constacyclic codes of length n over R are cyclic codes of length 2n over Z4. In many cases the latter codes have better parameters than ...

Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR(p,m) and generating sets for its ideals are considered. It is shown that these generating sets are strong Groebner bases. A method for finding ...

io-port 06440419 Chen, Jianzhang; Li, Jianping; Huang, Yuanyuan; Lin, Jie Some families of asymmetric quantum codes and quantum convolutional codes from constacyclic codes. Linear Algebra Appl. 475, 186-199 (2015). Summary: Quantum maximal-distance-separable (MDS) codes are an important class of quantum codes. Recently, many scholars utilize constacyclic codes to construct some quantum MDS code...

Let q be a prime power and Fq be a finite field. In this paper, we study constacyclic codes over the ring Fq + uFq + vFq + uvFq, where u 2 = u, v2 = v and uv = vu. We characterize the generator polynomials of constacyclic codes and their duals using some decomposition of this ring. Finally we study the images of self-dual cyclic codes over F2m + uF2m + vF2m + uvF2m through a linear Gray map.