One of the main challenges of coding theory is to construct linear codes with the best possible parameters. Various algebraic and combinatorial methods along with computer searches are used to construct codes with better parameters. Given the computational complexity of determining the minimum distance of a code, exhaustive searches are not feasible for all but small parameter sets. Therefore, ...

Let Fq be a finite field with q elements and denote by θ : Fq → Fq an automorphism of Fq. In this note, we deal with skew constacyclic codes, i.e. linear codes of Fnq which are invariant under the action of a semi-linear map T : Fnq → F n q , defined by T (a0, ..., an−2, an−1) := (αan−1, a0, ..., an−2) for some α ∈ Fq −{0} and n ≥ 2. In particular, we study some algebraic and geometric properti...

In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and constacyclic codes to be Galois LCD codes are characterized. Some illustrative examples which constacyclic codes are Galois LCD MDS codes are provided as well. In part...

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.

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...

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z 4 + uZ 4 of any length are studied. A new Gray map between Z 4 + uZ 4 and Z 4 (4) is defined. By means of this map, it is shown that the Z 4 Gray image of a (1 + u)-constacyclic code of length n over ...

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...