An Algebraic Approach for Decoding Spread Codes
Information Theory
2012-06-08 v4 math.IT
Abstract
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family of optimal codes with maximal minimum distance. We give a minimum-distance decoding algorithm which requires O((n-k)k^3) operations over an extension field F_{q^k}. Our algorithm is more efficient than the previous ones in the literature, when the dimension k of the codewords is small with respect to n. The decoding algorithm takes advantage of the algebraic structure of the code, and it uses original results on minors of a matrix and on the factorization of polynomials over finite fields.
Cite
@article{arxiv.1107.5523,
title = {An Algebraic Approach for Decoding Spread Codes},
author = {Elisa Gorla and Felice Manganiello and Joachim Rosenthal},
journal= {arXiv preprint arXiv:1107.5523},
year = {2012}
}