On the Bounds of Certain Maximal Linear Codes in a Projective Space

The set of all subspaces of F-q(n) is denoted by P-q(n). The subspace distance d(S)(X, Y) = dim(X) + dim(Y)-2dim(X boolean AND Y) defined on P-q(n) turns it into a natural coding space for error correction in random network coding. A subset of P-q(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of P-q(n). Braun et al. conjectured that the largest cardinality of a linear code, that contains F-q(n), is 2(n). In this paper, we prove this conjecture and characterize the maximal linear codes that contain F-q(n).

Quercetin, a Natural Flavonoid Interacts with DNA, Arrests Cell Cycle and Causes Tumor Regression by Activating Mitochondrial Pathway of Apoptosis

Naturally occurring compounds are considered as attractive candidates for cancer treatment and prevention. Quercetin and ellagic acid are naturally occurring flavonoids abundantly seen in several fruits and vegetables. In the present study, we evaluate and compare antitumor efficacies of quercetin and ellagic acid in animal models and cancer cell lines in a comprehensive manner. We found that quercetin induced cytotoxicity in leukemic cells in a dose-dependent manner, while ellagic acid showed only limited toxicity. Besides leukemic cells, quercetin also induced cytotoxicity in breast cancer cells, however, its effect on normal cells was limited or none. Further, quercetin caused S phase arrest during cell cycle progression in tested cancer cells. Quercetin induced tumor regression in mice at a concentration 3-fold lower than ellagic acid. Importantly, administration of quercetin lead to -5 fold increase in the life span in tumor bearing mice compared to that of untreated controls. Further, we found that quercetin interacts with DNA directly, and could be one of the mechanisms for inducing apoptosis in both, cancer cell lines and tumor tissues by activating the intrinsic pathway. Thus, our data suggests that quercetin can be further explored for its potential to be used in cancer therapeutics and combination therapy.