MDS and AMDS symbol-pair codes constructed from repeated-root codes

Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against the pair errors in symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable (MDS) symbol-pair codes that possess the largest possible pair-error correcting performance. Based on repeated-root cyclic codes, we construct two classes of MDS symbol-pair codes for more general generator polynomials and also give a new class of almost MDS (AMDS) symbol-pair codes with the length \(lp\). In addition, we derive all MDS and AMDS symbol-pair codes with length \(3p\), when the degree of the generator polynomials is no more than 10. The main results are obtained by determining the solutions of certain equations over finite fields.