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 \(q\ge 7\), 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.