Nov 2, 2023 · An ovoid, in the context of medical imaging, refers to a shape that resembles an elongated, symmetrically rounded form. This unique shape is instrumental in diagnosing and tracking changes in structures and tissues within the human body.

Ovoids of Q(4, q) are of special importance since from them we obtain spreads of W(3, q), which in turn give rise to symplectic translation planes. Ovoids of finite classical polar spaces are rare. They tend to exist only in classical polar spaces of low rank.

May 1, 2016 · A subset M of points of a generalized quadrangle Q is called an m-ovoid if every line of Q meets M in exactly m points. (Without giving the details we mention that m-ovoids of classical polar spaces can be defined similarly.) A 1-ovoid will be simply called an ovoid.

The objective of this article is to present a family of ovoids in PG(3,2m) from irreducible cyclic codes over GF(2 m ). Preprint submitted to Elsevier October 19, 2018

Mar 9, 2025 · Scientists at UBC have discovered a new type of brain cell, called ovoid cells, which play a key role in object recognition memory. This breakthrough could lead to new treatments for memory-related diseases like Alzheimer’s and epilepsy by targeting these cells to improve memory retention and prevent cognitive decline.

Feb 10, 2018 · Ovoids in $\PG (3, q)$ have been an interesting topic in coding theory, combinatorics, and finite geometry for a long time. So far only two families are known. The first is the elliptic quadratics and the second is the Tits ovoids.

Mar 25, 2019 · It is known that an ovoid in PG(3, GF(q)) corresponds to a [q 2 + 1, 4, q 2 - q] code over GF(q), which is called an ovoid code. The objectives of this paper are to develop the general theories of subfield codes and to study the subfield codes of the two families of ovoid codes.

So far only two families are known. The first is the elliptic quadratics and the second is the Tits ovoids. In this article, we present a family of ovoids in PG (3, 2 m) PG 3 superscript 2 𝑚 {\mathrm {PG}} (3,2^ {m}) for all m 𝑚 m which are from a family of irreducible cyclic codes.

2D shape—egg-shaped in outline, widest point is towards one end of the organ, the other end tapers gradually, attachment at or near the broad end (compare obovate, ovoid) and more attenuate at the narrow end.

Feb 15, 2024 · An ovoid in $\mathrm{PG}(3,q)$ is a set of $q^2+1$ points, no three of which are collinear. (Note that in [a2] and some other older publications, an ovoid is called an ovaloid.) If $q>2$, then an ovoid is a maximum-sized set of points, no three collinear, but in the case $q=2$ the complement of a plane is a set of $8$ points, no three collinear.