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In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely, we show that a GAG code is contained (up to isomorphism) in a suitable AG code. Next we recall the concept of an N1N2-automorphism group, a subgroup of the automorphism group of a GAG code. With the use of the relation we obtained between these two classes of codes, we show that the N1N2-automorphism group is a subgroup of the automorphism group of an AG code. [ABSTRACT FROM AUTHOR]

The use of natural agro-industrial materials as suspended fillers (SFs) in floating treatment wetlands (FTWs) to enhance nutrient removal performance has recently been gaining significant attention. However, the knowledge concerning the nutrient removal performance enhancement by different SFs (alone and in mixtures) and the major removal pathways is so far inadequate. The current research, for the first time, carried out a critical analysis using five different natural agro-industrial materials (biochar, zeolite, alum sludge, woodchip, flexible solid packing) as SFs in various FTWs of 20 L microcosm tanks, 450 L outdoor mesocosms, and a field-scale urban pond treating real wastewater over 180 d. The findings demonstrated that the incorporation of SFs in FTWs enhanced the removal performance of total nitrogen (TN) by 20–57% and total phosphorus (TP) by 23–63%. SFs further enhanced macrophyte growth and biomass production, leading to considerable increases in nutrient standing stocks. Although all the hybrid FTWs showed acceptable treatment performances, FTWs set up with mixtures of all five SFs significantly enhanced biofilm formation and enriched the abundances of the microbial community related to nitrification and denitrification processes, supporting the detected excellent N retention. N mass balance assessment demonstrated that nitrification-denitrification was the major N removal pathway in reinforced FTWs, and the high removal efficiency of TP was attributable to the incorporation of SFs into the FTWs. Nutrient removal efficiencies ranked in the following order among the various trials: microcosm scale (TN: 99.3% and TP: 98.4%) > mesocosm scale (TN: 84.0% and TP: 95.0%) > field scale (TN: −15.0–73.7% and TP: −31.5–77.1%). These findings demonstrate that hybrid FTWs could be easily scaled up for the removal of pollutants from eutrophic freshwater systems over the medium term in an environmentally-friendly way in regions with similar environmental conditions. Moreover, it demonstrates hybrid FTW as a novel way of disposing of significant quantities of wastes, showing a win-win means with a huge potential for large-scale application. [Display omitted] • Natural agro-industrial materials facilely incorporated into floating wetlands for enahanced nutrient removal. • A combined natural agro-industrial materials system improved N and P removal to an acceptable level. • Combination of various substrates enriched nutrient-related genera and improved micribial diversity. • Microbial action was the major mechanism for N removal from wastewater. • Hybrid FTW facilely up-scaled to eliminate N and P from eutrophic pond water. [ABSTRACT FROM AUTHOR]