On ZpZp[u, v]-additive cyclic and constacyclic codes

Let $\mathbb{Z}_{p}$ be the ring of residue classes modulo a prime $p$. The $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive cyclic codes of length $(\alpha,\beta)$ is identify as $\mathbb{Z}_{p}[u,v][x]$-submodule of $\mathbb{Z}_{p}[x]/\langle x^{\alpha}-1\rangle \times \mathbb{Z}_{p}[u,v][x]/\langle x^{\beta}-1\rangle$ where $\mathbb{Z}_{p}[u,v]=\mathbb{Z}_{p}+u\mathbb{Z}_{p}+v\mathbb{Z}_{p}$ with $u^{2}=v^{2}=uv=vu=0$. In this article, we obtain the complete sets of generator polynomials, minimal generating sets for cyclic codes with length $\beta$ over $\mathbb{Z}_{p}[u,v]$ and $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive cyclic codes with length $(\alpha,\beta)$ respectively. We show that the Gray image of $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive cyclic code with length $(\alpha,\beta)$ is either a QC code of length $4\alpha$ with index $4$ or a generalized QC code of length $(\alpha,3\beta)$ over $\mathbb{Z}_{p}$. Moreover, some structural properties like generating polynomials, minimal generating sets of $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive constacyclic code with length $(\alpha,p-1)$ are determined.Comment: It is submitted to the journa

Application of Basic Pharmacology and Dispensing Practice of Antibiotics in Accredited Drug-Dispensing Outlets in Tanzania.

Provision of pharmaceutical services in accredited drug-dispensing outlets (ADDOs) in Tanzania has not been reported. This study compared the antibiotics dispensing practice between ADDOs and part II shops, or duka la dawa baridi (DLDBs), in Tanzania. This was a cross-sectional study that was conducted in ADDOs and DLDBs. A simulated client method for data collection was used, and a total of 85 ADDOs, located in Mvomero, Kilombero, and Morogoro rural districts, were compared with 60 DLDBs located in Kibaha district. The research assistants posed as simulated clients and requested to buy antibiotics from ADDOs and DLDBs after presenting a case scenario or disease condition. Among the diseases presented were those requiring antibiotics and those usually managed only by oral rehydration salt or analgesics. The simulated clients wanted to know the antibiotics that were available at the shop. The posed questions set a convincing ground to the dispenser either to dispense the antibiotic directly, request a prescription, or refer the patient to a health facility. Proportions were used to summarize categorical variables between ADDOs and DLDBs, and the chi-square test was used to test for statistical difference between the two drug-outlet types in terms of antibiotic-dispensing practice. As many as 40% of trained ADDO dispensers no longer worked at the ADDO shops, so some of the shops employed untrained staff. A larger proportion of ADDOs than DLDBs dispensed antibiotics without prescriptions (P = 0.004). The overall results indicate that there was no difference between the two types of shops in terms of adhering to regulations for dispensing antibiotics. However, in some circumstances, eg, antibiotic sale without prescription and no referral made, for complicated cases, ADDOs performed worse than DLDBs. As many as 30% of DLDBs and 35% of ADDOs dispensed incomplete doses of antibiotics. In both ADDOs and DLDBs, fortified procaine penicillin powder was dispensed as topical application for injuries. There was no statistical difference between ADDOs and DLDBs in the violation of dispensing practice and both ADDOs and DLDBs expressed poor knowledge of the basic pharmacology of antibiotics