The most important results on C⊥ t (n, q), the dual code of points and t-spaces in PG(n, q) are presented. We focus on the minimum distance and on the small weight codewords. In the third section, a recent result about the classification of the small weight codewords in C⊥ n−1(n, q), q even, is given.

Definition 1. (directly density-reachable): A point p is directly density-reachable from a point q wrt. Eps, MinPts if 1. p ∈ NEps(q) and 2. |NEps(q)| ≥MinPts NEps(q) represents the Eps-neighborhood of the point q which includes all points whose distance to the point q is less than or equal to Eps. From the statement (2), it can be understood that there is a cluster if and only if there is a co...

As a generalization of BCH codes, constacyclic codes have become good source for constructing optimal codes. However, the parameters these are not easy to determine in general. In this paper, we investigate class $ q $-ary with length \frac{q^{m}+1}{2} and compute their exact dimensions some ranges designed distance. particular, study distance larger range than known results.

For any odd prime power q we first construct a certain non-linear binary code C(q, 2) having (q − q)/2 codewords of length q and weight (q − 1)/2 each, for which the Hamming distance between any two distinct codewords is in the range [q/2 − 3√q/2, q/2 + 3√q/2] that is, ‘almost constant’. Moreover, we prove that C(q, 2) is distance-invariant. Several variations and improvements on this theme are...

The Kerdock and extended Preparata codes are something of an enigma in coding theory since they are both Hamming-distance invariant and have weight enumerators that are MacWilliams duals just as if they were dual linear codes. In this paper, we explain, by constructing in a natural way a Preparata-like code PL from the Kerdock code K, why the existence of a distance-invariant code with weight d...

In this paper we discuss a relationship between the following two algebras: (i) the subconstituent algebra T of a distance-regular graph that has q-Racah type; (ii) the q-tetrahedron algebra ⊠q which is a q-deformation of the three-point sl2 loop algebra. Assuming that every irreducible T -module is thin, we display an algebra homomorphism from ⊠q into T and show that T is generated by the imag...

Suppose M is a compact orientable irreducible 3-manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized copy of P or the distance d(P) ≤ 2genus(Q). More generally, if P and Q are bicompressible but weakly incompressible connected closed separating surfaces in M then either • P and Q can be well-separated or • P and Q are isotopic or

Abstract Using gauge/gravity duality, we investigate the string breaking and dissolution of two heavy quarks coupled to a light quark at finite temperature. It is found that three configurations QQq exist with increase in separation distance for confined phase. Furthermore, occurs ( T 0.1\; {\rm{GeV}} ) decay mode {Q Q q} \rightarrow q q+Q \bar{q}} . In ...

In [16] K. Menger proposed the probabilistic concept of distance by replacing the number d(p, q), as the distance between points p, q, by a distribution function Fp,q. This idea led to development of probabilistic analysis [3], [11] [18]. In this paper, generalized probabilistic 2-normed spaces are studied and topological properties of these spaces are given. As an example, a space of random va...