Sum-rank product codes and bounds on the minimum distance
Information Theory
2021-06-01 v1 math.IT
Abstract
The tensor product of one code endowed with the Hamming metric and one endowed with the rank metric is analyzed. This gives a code which naturally inherits the sum-rank metric. Specializing to the product of a cyclic code and a skew-cyclic code, the resulting code turns out to belong to the recently introduced family of cyclic-skew-cyclic. A group theoretical description of these codes is given, after investigating the semilinear isometries in the sum-rank metric. Finally, a generalization of the Roos and the Hartmann-Tzeng bounds for the sum rank-metric is established, as well as a new lower bound on the minimum distance of one of the two codes constituting the product code.
Keywords
Cite
@article{arxiv.2105.15086,
title = {Sum-rank product codes and bounds on the minimum distance},
author = {Gianira N. Alfarano and F. J. Lobillo and Alessandro Neri and Antonia Wachter-Zeh},
journal= {arXiv preprint arXiv:2105.15086},
year = {2021}
}
Comments
18 pages