Partial Spreads in Random Network Coding

TL;DR

This paper introduces partial spread codes in random network coding, generalizing spread codes, with a focus on their description, maximality, and an efficient decoding algorithm.

Contribution

It presents a new class of network codes called partial spread codes, along with their matrix description, maximality analysis, and decoding method.

Findings

Partial spread codes generalize spread codes.

Efficient decoding algorithm is developed.

Descriptions of these codes are provided in matrix form.

Abstract

Following the approach by R. K\"otter and F. R. Kschischang, we study network codes as families of k-dimensional linear subspaces of a vector space F_q^n, q being a prime power and F_q the finite field with q elements. In particular, following an idea in finite projective geometry, we introduce a class of network codes which we call "partial spread codes". Partial spread codes naturally generalize spread codes. In this paper we provide an easy description of such codes in terms of matrices, discuss their maximality, and provide an efficient decoding algorithm.