DS and AMDS Symbol-Pair Codes from Three Families of Simple Root Cyclic Codes

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 $q\equiv 3(\mathrm{m}\mathrm{o}\mathrm{d}4)$ 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.