New Entanglement-Assisted Quantum MDS Codes with Maximal Entanglement

Abstract

The construction of maximum distance separable (MDS) linear complementary dual (LCD) codes and entanglement-assisted quantum MDS (EAQMDS) codes have been of a great interest. In this paper, for arbitrary prime power q, we construct two new families of MDS Hermitian LCD codes of length n = q(2)+1/lambda and n = q(2)-1/ r, where rq + 1. By applying the obtained MDS Hermitian LCD codes to the EAQMDS codes, we derive new maximal entanglement EAQMDS codes of parameters [[q(2)+1/lambda, q(2)+1/lambda - l + 1, l; l - 1]](q) where 2 <= l left perpendicular <= q(2)+1+2 lambda/2 lambda right perpendicular and [[q(2)-1/r, q(2)-1/r - gamma, gamma + 1; gamma]](q) where 1 <= gamma <= q(2)-1/2r