MDS and AMDS symbol-pair codes 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. Based on repeated-root cyclic codes, we construct two classes of MDS symbol-pair codes for more general generator polynomials and also give a new class of almost MDS (AMDS) symbol-pair codes with the length . In addition, we derive all MDS and AMDS symbol-pair codes with length , when the degree of the generator polynomials is no more than 10. The main results are obtained by determining the solutions of certain equations over finite fields.
Cite
@article{arxiv.2206.00462,
title = {MDS and AMDS symbol-pair codes constructed from repeated-root codes},
author = {Xiuxin Tang and Rong Luo},
journal= {arXiv preprint arXiv:2206.00462},
year = {2022}
}
Comments
22 pages. arXiv admin note: substantial text overlap with arXiv:2204.02670