Projective Reed–Muller type codes on rational normal scrolls

In this paper we study an instance of projective Reed–Muller type codes, i.e., codes obtained by the evaluation of homogeneous polynomials of a fixed degree in the points of a projective variety. In our case the variety is an important example of a determinantal variety, namely the projective surface known as rational normal scroll, defined over a finite field, which is the basic underlining algebraic structure of this work. We determine the dimension and a lower bound for the minimum distance of the codes, and in many cases we also find the exact value of the minimum distance. To obtain the results we use some methods from Gröbner bases theory.     

A new coding scheme of QC-LDPC codes for optical transmission systems

Based on Galois Field (GF(q)) multiplicative group, a new coding scheme for Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes is proposed, and the new coding scheme has some advantages such as the simpler construction, the easier implementation encoding, the lower complexity of the encoding and decoding, the more flexible adjustment of the code length as well as the code rate and so forth. Under the condition of considering the characteristics of optical transmission systems, an irregular QC-LDPC (3843,3603) code to be suitable for optical transmission systems is constructed by applying the proposed new coding scheme. The simulation result shows that the net coding gain (NCG) of the irregular QC-LDPC (3843,3603) code is respectively improved 2.14 dB, 1.19 dB, 0.24 dB and 0.14 dB more than those of the classic RS (255,239) code in ITU-T G.975, the LDPC (32640,30592) code in ITU-T G.975.1, the regular SCG-LDPC (3969,3720) code constructed by the Systematically Constructed Gallager (SCG) coding scheme and the regular QC-LDPC (4221,3956) code at the bit error rate (BER) of 10-8. Furthermore, all the five codes have the same code rate of 93.7%. Therefore, the irregular QC-LDPC (3843,3603) code constructed by the proposed new coding scheme has the more excellent error-correction performance and can be better suitable for optical transmission systems.     

The dual of a constacyclic code,self dual,reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings with nilpotency index 3

Over finite local Frobenius non-chain rings with nilpotency index 3 and when the length of the codes is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of $\gamma$-constacyclic codes is established and the algebraic characterization of self-dual $\gamma$-constacyclic codes, reversible $\gamma$-constacyclic codes and $\gamma$-constacyclic codes with complementary dual are given. Generators for the dual code are obtained from those of the original constacyclic code.     

Empirical Likelihood Estimation for the Two-Sample Mean under Density Ratio Models Using Auxiliary Information

Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and Lawless\ucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the dual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained by the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations.     

Weight enumerators of reducible cyclic codes and their dual codes

Let ${\mathbb{F}}_q$ be a finite field and $n$ a positive integer. In this paper, we find a new combinatorial method to determine weight enumerators of reducible cyclic codes and their dual codes of length $n$ over ${\mathbb{F}}_q$, which just generalize results of Zhu et al. (2015); especially, we also give the weight enumerator of a cyclic code, which is viewed as a partial Melas code. Furthermore, weight enumerators obtained in this paper are all in the form of power of a polynomial.     

Photoredox/Cobalt Dual-Catalyzed Decarboxylative Elimination of Carboxylic Acids: Development and Mechanistic Insight

Recently, dual-catalytic strategies towards the decarboxylative elimination of carboxylic acids have gained attention. Our lab previously reported a photoredox/cobaloxime dual catalytic method that allows the synthesis of enamides and enecarbamates directly from N-acyl amino acids and avoids the use of any stoichiometric reagents. Further development, detailed herein, has improved upon this transformation's utility and further experimentation has provided new insights into the reaction mechanism. These new developments and insights are anticipated to aid in the expansion of photoredox/cobalt dual-catalytic systems.     

Simultaneous separation and determination of seven isoflavones in Radix Puerariae by capillary electrophoresis with a dual cyclodextrin system

A simple, comprehensive and efficient capillary electrophoresis method using a dual cyclodextrin system was developed for the simultaneous determination of seven isoflavones (3′‐methoxypuerarin, puerarin, 3′‐hydroxypuerarin, ononin, daidzin, daidzein and genistin). Baseline separations of the seven isoflavones were achieved within 11 min with the running buffer consisting of 35 mm sodium tetraborate, 9.0 mm sulfobutylether‐β‐cyclodextrin and 30 mm α‐cyclodextrin at pH 9.34, and peaks were detected at 254 nm. Other separation parameters included the separation voltage for 15 kV and the working temperature for 25°C. Under the optimum conditions, good linearities were obtained with linear correlation coefficients of seven isoflavones of 0.9978–0.9992. The limits of detection and the limits of quantification were 0.7–2.9 and 2.5–9.5 μg/mL, respectively. Excellent precision and accuracy were obtained. The intraday and interday precision ranged from 0.7 to 2.0% and from 0.8 to 1.9%, respectively. The recoveries of seven analytes were from 97.7 to 103.1%. This method was successfully applied to determine the seven analytes in Radix Puerariae and its preparations.