16357873
Secret sharing schemes from three classes of linear codes
Secret sharing has been a subject of study for over 20 years, and has had a number of real-world applications. There are several approaches to the construction of secret sharing schemes. One of them is based on coding theory. In principle, every linear code can be used to construct secret sharing schemes. But determining the access structure is very hard as this requires the complete characterization of the minimal codewords of the underlying linear code, which is a difficult problem in general. In this paper, a sufficient condition for all nonzero codewords of a linear code to be minimal is derived from exponential sums. Some linear codes whose covering structure can be determined are constructed, and then used to construct secret sharing schemes with nice access structures.
18916806
The weight distribution of a class of linear codes from perfect nonlinear functions
In this correspondence, the weight distribution of a class of linear codes based on perfect nonlinear functions (also called planar functions) is determined. The class of linear codes under study are either optimal or among the best codes known, and have nice applications in cryptography.
20645165
Harper-type lower bounds and the bandwidths of the compositions of graphs
Abstract We give a general Harper-type lower bound for the bandwidth of a graph which is a common generalization of several known results. As applications we get a lower bound for the bandwidth of the composition of two graphs. By using this we determine the bandwidths of some composition graphs such as ( P r × P s )[ H ], ( P r × C s )[ H ] (2 r ≠ s ), ( C r × C s )[ H ] (6 ⩽ 2 r ⩽ s ), etc., for any graph H . Interestingly, the bandwidths of these graphs have nothing to do with the structure of H in general.
45614324
Partition the vertices of a graph into one independent set and one acyclic set
For a given graph G, if the vertices of G can be partitioned into an independent set and an acyclic set, then we call G a near-bipartite graph. This paper studies the recognition of near-bipartite graphs. We give simple characterizations for those near-bipartite graphs having maximum degree at most 3 and those having diameter 2. We also show that the recognition of near-bipartite graphs is NP-complete even for graphs where the maximum degree is 4 or where the diameter is 4.
15379720
Enhanced homology searching through genome reading frame predetermination
MOTIVATION
Many bioinformatic approaches exist for finding novel genes within genomic sequence data. Traditionally, homology search-based methods are often the first approach employed in determining whether a novel gene exists that is similar to a known gene. Unfortunately, distantly related genes or motifs often are difficult to find using single query-based homology search algorithms against large sequence datasets such as the human genome. Therefore, the motivation behind this work was to develop an approach to enhance the sensitivity of traditional single query-based homology algorithms against genomic data without losing search selectivity.


RESULTS
We demonstrate that by searching against a genome fragmented into all possible reading frames, the sensitivity of homology-based searches is enhanced without degrading its selectivity. Using the ETS-domain, bromodomain and acetyl-CoA acetyltransferase gene as queries, we were able to demonstrate that direct protein-protein searches using BLAST2P or FASTA3 against a human genome segmented among all possible reading frames and translated was substantially more sensitive than traditional protein-DNA searches against a raw genomic sequence using an application such as TBLAST2N. Receiver operating characteristic analysis was employed to demonstrate that the algorithms remained selective, while comparisons of the algorithms showed that the protein-protein searches were more sensitive in identifying hits. Therefore, through the overprediction of reading frames by this method and the increased sensitivity of protein-protein based homology search algorithms, a genome can be deeply mined, potentially finding hits overlooked by protein-DNA searches against raw genomic data.