Rank errorcorrecting pairs
Abstract
Errorcorrecting pairs were introduced independently by Pellikaan and Kötter as a general method of decoding linear codes with respect to the Hamming metric using coordinatewise products of vectors, and are used for many wellknown families of codes. In this paper, we define new types of vector products, extending the coordinatewise product, some of which preserve symbolic products of linearized polynomials after evaluation and some of which coincide with usual products of matrices. Then we define rank errorcorrecting pairs for codes that are linear over the extension field and for codes that are linear over the base field, and relate both types. Bounds on the minimum rank distance of codes and MRD conditions are given. Finally we show that some wellknown families of rankmetric codes admit rank errorcorrecting pairs, and show that the given algorithm generalizes the classical algorithm using errorcorrecting pairs for the Hamming metric.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.08144
 Bibcode:
 2015arXiv151208144M
 Keywords:

 Computer Science  Information Theory;
 15B33;
 94B35;
 94B65