Polyadic Constacyclic Codes

For any given positive integer $m$, a necessary and sufficient condition for the existence of Type I $m$-adic constacyclic codes is given. Further, for any given integer $s$, a necessary and sufficient condition for $s$ to be a multiplier of a Type I polyadic constacyclic code is given. As an application, some optimal codes from Type I polyadic constacyclic codes, including generalized Reed-Solomon codes and alternant MDS codes, are constructed.Comment: We provide complete solutions on two basic questions on polyadic constacyclic cdes, and construct some optimal codes from the polyadic constacyclic cde

Recent progress on weight distributions of cyclic codes over finite fields

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. In coding theory it is often desirable to know the weight distribution of a cyclic code to estimate the error correcting capability and error probability. In this paper, we present the recent progress on the weight distributions of cyclic codes over finite fields, which had been determined by exponential sums. The cyclic codes with few weights which are very useful are discussed and their existence conditions are listed. Furthermore, we discuss the more general case of constacyclic codes and give some equivalences to characterize their weight distributions

Skew Constacyclic Codes over Finite Fields and Finite Chain Rings

This paper overviews the study of skew Θ-λ-constacyclic codes over finite fields and finite commutative chain rings. The structure of skew Θ-λ-constacyclic codes and their duals are provided. Among other results, we also consider the Euclidean and Hermitian dual codes of skew Θ-cyclic and skew Θ-negacyclic codes over finite chain rings in general and over Fpm+uFpm in particular. Moreover, general decoding procedure for decoding skew BCH codes with designed distance and an algorithm for decoding skew BCH codes are discussed

In Vitro Corrosion Properties of Mg Matrix In Situ Composites Fabricated by Spark Plasma Sintering

Mg matrix in situ composites were fabricated from Mg and ZnO powder by a spark plasma sintering method. The composition and microstructure of the sintered samples were characterized. Corrosion properties of fabricated composites were evaluated by immersion and by electrochemical tests using Hanks’ solution. The results showed that the formation of in situ products improved significantly the corrosion resistance of the fabricated composites compared with pure Mg; Mg-10 wt % ZnO composites especially exhibited the lowest corrosion rate. In addition, an energy-dispersive X-ray (EDX) analysis showed that calcium phosphate formed as a corrosion product on the surface of Mg-10 wt % ZnO composites, while Mg(OH)_2 appeared as a corrosion product on the surface of Mg-20 wt % ZnO composite. The findings suggested Mg-10 wt % ZnO composite as a potential candidate for temporary implant application