Related papers: A new partial geometry pg(5,5,2)
Twelve new strongly regular graphs with parameters (81,30,9,12) are found as graphs invariant under certain subgroups of the automorphism groups of the two previously known graphs that arise from 2-weight codes. One of these new graphs is…
We determine that there is no partial geometry ${\cal G}$ with parameters $(s,t,\alpha)=(4,27,2)$. The existence of such a geometry has been a challenging open problem of interest to researchers for almost 40 years. The particular interest…
The subject of this paper are partial geometries $pg(s,t,\alpha)$ with parameters $s=d(d'-1), \ t=d'(d-1), \ \alpha=(d-1)(d'-1)$, $d, d' \ge 2$. In all known examples, $q=dd'$ is a power of 2 and the partial geometry arises from a maximal…
A new family of commutative semifields with two parameters is presented. Its left and middle nucleus are both determined. Furthermore, we prove that for any different pairs of parameters, these semifields are not isotopic. It is also shown…
In this paper we construct new Griesmer codes of dimension $k\geq 5$ by means of some geometric methods such as projective dual and geometric puncturing.
New families of Cameron-Liebler line classes of ${\rm PG}(3,q)$, $q\ge 7$ odd, with parameter $(q^2+1)/2$ are constructed.
An informal introduction to some new geometric partial differential equations motivated by string theories is provided. Some of these equations are also interesting from the point of view of non-K\"ahler geometry and the theory of…
The classification of all semiovals and blocking semiovals in $\mathrm{PG}(2,8)$ and in $\mathrm{PG}(2,9)$ of size less than $17$ is determined. Also, some information on the stabilizer groups and the intersection sizes with lines is given.
We construct a new family of strongly regular graphs with the same parameters as the strongly regular graphs $D_{5,5}(q)$. The construction can be seen as a variant of the construction of twisted Grassmann graphs by Van Dam and Koolen.
In this article we construct a series of new infinite families of strongly regular graphs with the same parameters as the point-graphs of non-singular quadrics in PG(n,2).
In this paper, using group actions, we introduce a new method for constructing partial geometric designs (sometimes referred to as $1\frac{1}{2}$-designs). Using this new method, we construct several infinite families of partial geometric…
Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi\'{c}'s and Winkler's relations play an important role in the theory of partial cubes. These structures are employed in the…
We provide a geometrical construction of the slim dense near hexagon with parameters $(s,t,t_{2})=(2,5,\{1,2\})$. Using this construction, we construct the rank 3 symplectic dual polar space $DSp(6,2)$ which is the slim dense near hexagon…
We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs…
This letter establishes a procedure which can determine an algebra of exotic particles obeying fractional statistics and living in two-dimensional space using a non-commuting coordinates.
The use of partial geometries to construct parity-check matrices for LDPC codes has resulted in the design of successful codes with a probability of error close to the Shannon capacity at bit error rates down to $10^{-15}$. Such…
New upper bounds on the smallest size t_{2}(2,q) of a complete arc in the projective plane PG(2,q) are obtained for 853<= q<= 2879 and q=3511,4096, 4523,5003,5347,5641,5843,6011. For q<= 2377 and q=2401,2417,2437, the relation…
In this work, we prove the existence of maximal partial line spreads in PG(5,q) of size q^3+q^2+kq+1, with 1 \leq k \leq (q^3-q^2)/(q+1), k an integer. Moreover, by a computer search, we do this for larger values of k, for q \leq 7. Again…
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…