AMDS symbol-pair codes from repeated-root cyclic codes

作者：Ma, Junru; Luo, Jinquan^*

来源：Discrete Mathematics, 2023, 346(7): 113391.

DOI：10.1016/j.disc.2023.113391

• AMDS symbol-pair codes
• Minimum symbol-pair distance
• Cyclic codes
• Repeated-root cyclic codes

Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. One of the central themes in symbol-pair coding theory is the constructions of symbol-pair codes with the largest possible minimum symbol-pair distance. Maximum distance separable (MDS) and almost maximum distance separable (AMDS) symbol-pair codes are optimal and sub-optimal regarding the Singleton bound, respectively. In this paper, six new classes of AMDS symbol-pair codes are explicitly constructed through repeated-root cyclic codes. Remarkably, one class of such codes has unbounded lengths and the minimum symbol-pair distance of another class can reach 13.