Quantum AMDS negacyclic codes of length 2ps over Fpm

In this article, we investigate all almost maximum distance separable (briefly, AMDS) negacyclic codes of length 2p^s over the finite field F_p^m, where p is an odd prime. A necessary and sufficient condition for a code to be an AMDS and NMDS negacyclic code of length 2p^s over F_p^m is also provided. In addition, we construct quantum AMDS (qAMDS) codes using both the Calderbank-Shor-Steane (CSS) and Hermitian constructions. These newly constructed codes have different parameters compared to previous constructions. Moreover, our qAMDS codes are better than all known quantum error correction (QEC) codes.