PreprintCC BY 4.0arXiv
DS and AMDS Symbol-Pair Codes from Three Families of Simple Root Cyclic Codes
Abstract
Symbol-pair distances of simple-root cyclic codes are important for evaluating error correction performance under overlapping pair read channels. In this paper, we construct three families of simple-root cyclic codes over finite fields of odd characteristic via generator polynomials. For length 2q+2, the minimum symbol-pair distance is 10 for every odd prime power q≥ 7, established by excluding invalid support configurations. For length 4q−4, when q≡ 3pmod 4 and finite field constraints hold, it is 9 or 10. For length 2(q−1), reciprocal-polynomial analysis shows it is 11 or 12. All obtained codes are MDS or AMDS symbol-pair codes.
Related
- On the b-Symbol Weight Distribution of Dual Melas Codes and a Poisson Randomness Postulate
- Data Protection in Function-Correcting Symbol-Pair Codes: Redundancy Bounds and Protection Profiles
- Function-Correcting Lee-distance Codes for Symbol-Pair Read Channels
- New distance bounds for one-generator quasi-cyclic codes with applications to Hermitian LCD codes and entanglement-assisted quantum codes
- New families of additive non-RS MDS codes and ACD codes from twisted Reed-Solomon codes
BibTeX
@misc{he2026amds,
title = {{DS and AMDS Symbol-Pair Codes from Three Families of Simple Root Cyclic Codes}},
author = {Jiawei He and Zihan Zhang and Xiaoqiang Wang and Zhao Lin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14435},
eprint = {2610.14435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14435},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - DS and AMDS Symbol-Pair Codes from Three Families of Simple Root Cyclic Codes
AU - Jiawei He
AU - Zihan Zhang
AU - Xiaoqiang Wang
AU - Zhao Lin
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14435
UR - https://arxiv.org/abs/2610.14435
AB - Symbol-pair distances of simple-root cyclic codes are important for evaluating error correction performance under overlapping pair read channels. In this paper, we construct three families of simple-root cyclic codes over finite fields of odd characteristic via generator polynomials. For length 2q+2, the minimum symbol-pair distance is 10 for every odd prime power q≥ 7, established by excluding invalid support configurations. For length 4q−4, when q≡ 3pmod 4 and finite field constraints hold, it is 9 or 10. For length 2(q−1), reciprocal-polynomial analysis shows it is 11 or 12. All obtained codes are MDS or AMDS symbol-pair codes.
ER -