New cyclic codes improve error correction for overlapping symbol pairs
DS and AMDS Symbol-Pair Codes from Three Families of Simple Root Cyclic Codes
Information TheoryCryptography and Security
Summary
When data is read in overlapping pairs, errors can be tricky to detect and fix. The authors studied special cyclic codes to measure how well they correct mistakes in these overlapping pairs. They created three groups of codes that work over certain finite fields and have good minimum distances, which means better error detection and correction ability. Their codes are either maximum distance separable (MDS) or almost MDS, meaning they perform very well for their size. This work helps in understanding and building better coding methods for certain communication channels.
What this means in practice
- •For communication system engineers: Design error-correcting codes for channels reading data in overlapping pairs using the new cyclic codes with proven high minimum symbol-pair distances.
- •For data storage hardware teams: Implement robust error correction in storage devices where data retrieval involves pair overlaps by utilizing these MDS and AMDS symbol-pair codes.
Authors
Jiawei He, Zihan Zhang, Xiaoqiang Wang, Zhao Lin
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 \(q\ge 7\), established by excluding invalid support configurations. For length \(4q-4\), when \(q\equiv 3\pmod 4\) 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.