We survey some old and some new characterizations of distance-regular graphs, which depend on information retrieved from their adjacency matrix. In particular, it is shown that a regular graph with d+ 1 distinct eigenvalues is distance-regular if and only if a numeric equality, involving only the spectrum of the graph and the numbers of vertices at distance d from each vertex, is satisfied.

Article history: Received 22 May 2014 Accepted 8 November 2014 Available online 25 November 2014 Submitted by J.M. Landsberg MSC: 15B99 13P25 20G20

Various methods have been used to obtain improvements of the Goppa lower bound for the minimum distance of an algebraic geometric code. The main methods divide into two categories and all but a few of the known bounds are special cases of either the Lundell-McCullough floor bound or the Beelen order bound. The exceptions are recent improvements of the floor bound by Güneri-Stichtenoth-Taskin, a...

Recent years have seen an increasing interest in algebraic curves and surfaces of high degree as geometric models or shape descriptors for model-based computer vision tasks such as object recognition and position estimation. Although their invariant-theoretic properties them a natural choice for these tasks, fitting algebraic curves and surfaces to data sets is difficult, and fitting algorithms...

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Finding the minimum distance of linear codes is one main problems in coding theory. The importance comes from its error-correcting and error-detecting capability handled codes. It was proven that this problem an NP-hard solution can be guessed verified polynomial time but no particular rule followed to make guess some meta-heuristic approaches literature have been used solve problem. In paper, ...

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