Locally Recoverable Codes correcting many erasures over small fields

We define linear codes which are s-Locally Recoverable Codes (or s-LRC), i.e. codes which are LRC in s ways, the case $$s=1$$ s = 1 roughly corresponding to the classical case of LRC codes. We use them to describe codes which correct many erasures, although they have small minimum distance. Any letter of a received word may be corrected using s different local codes. We use the Segre embedding of s local codes and then a linear projection.

Convolution of Riemannian manifolds and its applications

It is well-known that warped products play some important roles in differential geometry as well as in physics. In this article we extend the notion of warped product to the notion of convolution of Riemannian manifolds. We study the basic properties of convolutions of Riemannian manifolds. We also apply the notion of convolution to establish and characterise the Euclidean version of Segre embedding.