Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get q-ary quantum MDS codes, it suffices to find linear MDS codes C over F q 2 satisfying C ⊥ H ⊆ C by the Hermitian construction and the quantum Singleton bound. If C ⊥ H ⊆ C, we say that C is a dual-containing code. Many new quantum MDS codes with relatively large minimum distance have been produced by constructing dual-containing constacyclic MDS codes (see [18], [24], [25]). These works motivate us to make a careful study on the existence condition for nontrivial dual-containing constacyclic codes. This would help us to avoid unnecessary attempts and provide effective ideas in order to construct dual-containing codes. Several classes of dual-containing MDS constacyclic codes are constructed and their parameters are computed. Consequently, new quantum MDS codes are derived from these parameters. The quantum MDS codes exhibited here have parameters better than the ones available in the literature.

An equivalence relation called isometry is introduced to classify constacyclic codes over a finite field; the polynomial generators of constacyclic codes of length ℓ t p s are characterized, where p is the characteristic of the finite field and ℓ is a prime different from p.

Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This application of LCD codes renewed the interest in the construction of LCD codes having a large minimum distance. MDS codes are optimal in the sense that the minimum distance cannot be improved for given length and code size. Constructing LCD MDS codes is thus of significance in theory and practice. Recently, Jin ([8], IEEE Trans. Inf. Theory, 2016) constructed several classes of LCD MDS codes through generalized Reed-Solomon codes. In this paper, a different approach is proposed to obtain new LCD MDS codes from generalized Reed-Solomon codes. Consequently, new code constructions are provided and certain previously known results in [8] are extended.

Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pair errors the code can correct. MDS symbol-pair codes are optimal in the sense that pair distance cannot be improved for given length and code size. The contribution of this paper is twofold. First we present three lower bounds for the minimum pair distance of constacyclic codes, the first two of which generalize the previously known results due to Cassuto and Blaum (2011) and Kai et al. (2015). The third one exhibits a lower bound for the minimum pair distance of repeated-root cyclic codes. Second we obtain new MDS symbol-pair codes with minimum pair distance seven and eight through repeated-root cyclic codes.

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A delay in the mechanical transplantation (MT) of rice seedlings frequently occurs in Huanghuai wheat-rice rotation cropping districts of China, due to the late harvest of wheat, the poor weather conditions and the insufficiency of transplanters, missing the optimum transplanting time and causing seedlings to age. To identify how delaying transplanting rice affects the agronomic characteristics including the growth duration, photosynthetic productivity and dry matter remobilization efficiency and the grain yield under mechanical transplanting pattern, an experiment with a split-plot design was conducted over two consecutive years. The main plot includes two types of cultivation: mechanical transplanting and artificial transplanting (AT). The subplot comprises four japonica rice cultivars. The results indicate that the rice jointing, booting, heading and maturity stages were postponed under MT when using AT as a control. The tiller occurrence number, dry matter weight per tiller, accumulative dry matter for the population, leaf area index, crop growth rate, photosynthetic potential, and dry matter remobilization efficiency of the leaf under MT significantly decreased compared to those under AT. In contrast, the reduction rate of the leaf area during the heading-maturity stage was markedly enhanced under MT. The numbers of effective panicles and filled grains per panicle and the grain yield significantly decreased under MT. A significant correlation was observed between the dry matter production, remobilization and distribution characteristics and the grain yield. We infer that, as with rice from old seedlings, the decrease in the tiller occurrence, the photosynthetic productivity and the assimilate remobilization efficiency may be important agronomic traits that are responsible for the reduced grain yield under MT.

Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional properties that can be applied efficiently in encoding and decoding algorithms. It is desirable to find cyclic constant dimension codes such that both the code sizes and the minimum distances are as large as possible. In this paper, we explore the ideas of constructing cyclic constant dimension codes proposed in [2], IEEE Trans. Inf. Theory, 2016 and [17], Des. Codes Cryptogr., 2016 to obtain further results. Consequently, new code constructions are provided and several previously known results in [2] and [17] are extended.