MDS and AMDS symbol-pair codes are constructed from repeated-root codes
Abstract
Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against the pair errors in symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable (MDS) symbol-pair codes that possess the largest possible pair-error correcting performance. In this paper, we construct more general generator polynomials for two classes of MDS symbol-pair codes with code length . Based on repeated-root cyclic codes, we derive all MDS symbol-pair codes of length , when the degree of the generator polynomials is no more than 10. We also give two new classes of (almost maximal distance separable) AMDS symbol-pair codes with the length or by virtue of repeated-root cyclic codes. For length , we derive all AMDS symbol-pair codes, when the degree of the generator polynomials is less than 10. The main results are obtained by determining the solutions of certain equations over finite fields.
Cite
@article{arxiv.2204.02670,
title = {MDS and AMDS symbol-pair codes are constructed from repeated-root codes},
author = {Xiuxin Tang and Rong Luo},
journal= {arXiv preprint arXiv:2204.02670},
year = {2022}
}
Comments
27 pages. arXiv admin note: text overlap with arXiv:2010.04329 by other authors