Entanglement-assisted quantum codes from arbitrary binary linear codes

It is possible to construct an entanglement-assisted quantum error-correcting (EAQEC, for short) code from any classical linear code. However, the parameter of ebits $$c$$c is usually calculated by computer search. In this work, we can construct a family of $$[[2n-k, k, \ge d; c]]$$[[2n-k,k,≥d;c]] EAQEC codes from arbitrary binary $$[n, k, d]$$[n,k,d] linear codes, where the parameter of ebits $$c=2n-2k$$c=2n-2k can be easily generated algebraically and not by computational search. Moreover, the constructed EAQEC codes are maximal-entanglement EAQEC codes. We also present a different method of constructing entanglement-assisted accumulator codes. Finally, we prove that asymptotically good EAQEC codes exist.