Self-dual codes over F_q+uF_q+u^2 F_q and applications

Self-dual codes over finite fields and over some finite rings have been of interest and extensively studied due to their nice algebraic structures and wide applications. Recently, characterization and enumeration of Euclidean self-dual linear codes over the ring~$\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}$ with $u^3=0$ have been established. In this paper, Hermitian self-dual linear codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}$ are studied for all square prime powers~$q$. Complete characterization and enumeration of such codes are given. Subsequently, algebraic characterization of $H$-quasi-abelian codes in $\mathbb{F}_q[G]$ is studied, where $H\leq G$ are finite abelian groups and $\mathbb{F}_q[H]$ is a principal ideal group algebra. General characterization and enumeration of $H$-quasi-abelian codes and self-dual $H$-quasi-abelian codes in $\mathbb{F}_q[G]$ are given. For the special case where the field characteristic is $3$, an explicit formula for the number of self-dual $A\times \mathbb{Z}_3$-quasi-abelian codes in $\mathbb{F}_{3^m}[A\times \mathbb{Z}_3\times B]$ is determined for all finite abelian groups $A$ and $B$ such that $3\nmid |A|$ as well as their construction. Precisely, such codes can be represented in terms of linear codes and self-dual linear codes over $\mathbb{F}_{3^m}+u\mathbb{F}_{3^m}+u^2\mathbb{F}_{3^m}$. Some illustrative examples are provided as well

Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras

The main focus of this paper is the complete enumeration of self-dual abelian codes in nonprincipal ideal group algebras F2k[A×Z2×Z2s] with respect to both the Euclidean and Hermitian inner products, where k and s are positive integers and A is an abelian group of odd order. Based on the well-known characterization of Euclidean and Hermitian self-dual abelian codes, we show that such enumeration can be obtained in terms of a suitable product of the number of cyclic codes, the number of Euclidean self-dual cyclic codes, and the number of Hermitian self-dual cyclic codes of length 2s over some Galois extensions of the ring F2k+uF2k, where u2=0. Subsequently, general results on the characterization and enumeration of cyclic codes and self-dual codes of length ps over Fpk+uFpk are given. Combining these results, the complete enumeration of self-dual abelian codes in F2k[A×Z2×Z2s] is therefore obtained

Evaluating the Prebiotic Properties of Agar Oligosaccharides Obtained from the Red Alga <i>Gracilaria fisheri</i> via Enzymatic Hydrolysis

Currently, the demand in the food market for oligosaccharides with biological activities is rapidly increasing. In this study, agar polysaccharides from Gracilaria fisheri were treated with β-agarases and hydrolyzed to agar oligosaccharides (AOSs). High-performance anion-exchange chromatography/pulsed amperometric detection (HPAEC-PAD), Fourier-transform infrared spectroscopy (FT-IR), and gel permeation chromatography (GPC), were employed to analyze the chemical characteristics of AOSs. The FT-IR spectra revealed that the enzymatic hydrolysis had no effect on specific functional groups in the AOS molecule. To investigate the prebiotic and pathogen inhibitory effects of AOSs, the influence of AOSs on the growth of three probiotic and two pathogenic bacteria was examined. The gastrointestinal tolerance of probiotics in the presence of AOSs was also investigated. AOSs enhanced the growth of Lactobacillus plantarum by 254%, and inhibited the growth of Bacillus cereus by 32.80%, and Escherichia coli by 58.94%. The highest survival rates of L. plantarum and L. acidophilus were maintained by AOSs in the presence of α-amylase and HCl under simulated gastrointestinal conditions. This study demonstrates that AOSs from G. fisheri exhibit potential as a prebiotic additive in foods

Inhibitory Effects of <i>Caulerpa racemosa</i>, <i>Ulva intestinalis</i>, and <i>Lobophora challengeriae</i> on Tyrosinase Activity and α-MSH-Induced Melanogenesis in B16F10 Melanoma Cells

Melanogenesis involves a synthesis of melanin pigment and is regulated by tyrosinase. The addition of whitening agents with tyrosinase-inhibiting properties in cosmetics is becoming increasingly important. In this study, the ethanolic extracts from twelve seaweeds were assessed for tyrosinase-inhibiting activity using mushroom tyrosinase and melanin synthesis in B16F10 melanoma cells. The highest mushroom tyrosinase inhibition (IC50) was observed with Lobophora challengeriae (0.15 ± 0.01 mg mL−1); treatment was more effective than kojic acid (IC50 = 0.35 ± 0.05 mg mL−1), a well-known tyrosinase inhibitor. Three seaweeds, Caulerpa racemosa, Ulva intestinalis, and L. challengeriae, were further investigated for their ability to reduce melanogenesis in B16F10 cells. The ethanolic extracts of C. racemosa, U. intestinalis, and L. challengeriae showed inhibitory effects by reducing melanin and intracellular tyrosinase levels in B16F10 cells treated with α-melanocyte stimulating hormone in a dose-dependent manner. C. racemosa (33.71%) and L. challengeriae (36.14%) at 25 µg mL−1 reduced melanin production comparable to that of kojic acid (36.18%). L. challengeriae showed a stronger inhibition of intracellular tyrosinase (decreased from 165.23% to 46.30%) than kojic acid (to 72.50%). Thus, ethanolic extracts from C. racemosa, U. intestinalis, and L. challengeriae can be good sources of natural tyrosinase inhibitors and therapeutic or cosmetic agents in the future