English

MDS and AMDS symbol-pair codes constructed from repeated-root codes

Information Theory 2022-06-02 v1 math.IT

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 lplp. In addition, we derive all MDS and AMDS symbol-pair codes with length 3p3p, 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.

Keywords

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

R2 v1 2026-06-24T11:35:55.198Z