The distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum Hamming distance. Considering convenience for encoding, we focus on the distance profiles with respect to cyclic subcode chains (DPCs) of cyclic codes over GF (q) with length n such that gcd(n, ...

The probability that two spatial objects establish some kind of mutual connection often depends on their proximity. To formalize this concept, we define the notion of a probabilistic neighborhood : Let P be a set of n points in R, q ∈ R a query point, dist a distance metric, and f : R → [0, 1] a monotonically decreasing function. Then, the probabilistic neighborhood N(q, f) of q with respect to...

A nonlinear code can be represented as the union of cosets of a linear subcode. Properties and constructions of new codes from given ones in terms of this representation can be described. Algorithms to compute the minimum distance of nonlinear codes, based on known algorithms for linear codes, are also established. Moreover, the performance of these algorithms is studied and an estimation of th...

We obtain the following characterization of Q-polynomial distance-regular graphs. Let Γ denote a distance-regular graph with diameter d ≥ 3. Let E denote a minimal idempotent of Γ which is not the trivial idempotent E0. Let {θ∗ i }i=0 denote the dual eigenvalue sequence for E. We show that E is Q-polynomial if and only if (i) the entry-wise product E ◦ E is a linear combination of E0, E, and at...

In his famous theorem (1982), Douglas Leonard characterized the q-Racah polynomials and their relatives in the Askey scheme from the duality property of Q-polynomial distance-regular graphs. In this paper we consider a nonsymmetric (or Laurent) version of the q-Racah polynomials in the above situation. Let Γ denote a Q-polynomial distance-regular graph that contains a Delsarte clique C. Assume ...

This paper starts with a study of the minimum of the Rényi divergence subject to a fixed (or minimal) value of the total variation distance. Relying on the solution of this minimization problem, we determine the exact region of the points ( D(Q||P1), D(Q||P2) ) where P1 and P2 are any probability distributions whose total variation distance is not below a fixed value, and the probability distri...

There has been considerable interest in similarity join in the research community recently. Similarity join is a fundamental operation in many application areas, such as data integration and cleaning, bioinformatics, and pattern recognition. We focus on efficient algorithms for similarity join with edit distance constraints. Existing approaches are mainly based on converting the edit distance c...

Finding the similarity between paths is an important problem that comes up in many areas such as 3D modeling, GIS applications, ordering, and reachability. Given a set of points S, a polygonal curve P , and an ε > 0, the discrete set-chain matching problem is to find another polygonal curve Q such that the nodes of Q are points in S and dF (P,Q) ≤ ε. Here, dF is the discrete Fréchet distance be...