Your Search Results

Use this resource - and many more! - in your textbook!

AcademicPub holds over eight million pieces of educational content for you to mix-and-match your way.

Experience the freedom of customizing your course pack with AcademicPub!
Not an educator but still interested in using this content? No problem! Visit our provider's page to contact the publisher and get permission directly.

A basis for all solutions of the key equation for Gabidulin codes

By: Bossert, M.; Sidorenko, V.; Wachter, A.;

2010 / IEEE / 978-1-4244-7892-7

Description

This item was taken from the IEEE Conference ' A basis for all solutions of the key equation for Gabidulin codes ' We present and prove the correctness of an efficient algorithm that provides a basis for all solutions of a key equation in order to decode Gabidulin (G-) codes up to a given radius � This algorithm is based on a symbolic equivalent of the Euclidean Algorithm (EA) and can be applied for decoding of G-codes beyond half the minimum rank distance. If the key equation has a unique solution, our algorithm reduces to Gabidulin's decoding algorithm up to half the minimum distance. If the solution is not unique, we provide a basis for all solutions of the key equation. Our algorithm has time complexity O(�sup>2) and is a generalization of the modified EA by Bossert and Bezzateev for Reed-Solomon codes.