Spread Decoding in Extension Fields

TL;DR

This paper introduces a new representation of spread codes in extension fields and proposes an efficient decoding algorithm optimized for scenarios with small-dimensional codewords, received spaces, and error spaces.

Contribution

It presents a novel spread code representation and a corresponding minimum distance decoding algorithm tailored for low-dimensional cases.

Findings

Decoding algorithm is efficient for small dimensions

New spread code representation simplifies decoding process

Improved decoding performance in specific low-dimensional scenarios

Abstract

A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we present a new representation of spread codes with a minimum distance decoding algorithm which is efficient when the codewords, the received space and the error space have small dimension.