Maximal entanglement entanglement-assisted quantum codes from quaternary BCH codes

Abstract

Maximal entanglement entanglement-assisted quantum error correcting codes (EAQECCs) can achieve the EA-hashing bound asymptotically, and a higher rate and/or better noise suppression capabilities may be achieved by exploiting maximal entanglement. In this work, we discuss construction of some families of [n, k, d] zero radical codes with minimal distance d ≥ 6, 8, 10, 12, 14 from two classes of quaternary Bose-Chaudhuri-Hocquenghem (BCH) codes. Using these zero radical codes, we construct many maximal entanglement EAQECCs with very good parameters. We calculate the parameters of these EAQECCs by easily algebraical method, rather than by usually method of computation by computer. The maximal entanglement EAQECCs presented here have better parameters than those available in the literature.

Entanglement-Assisted Quantum Codes from Cyclic Codes

“…As an example, the code [ [16, 3, 9; 3]] 4 has a higher rate (ratio between code dimension and code length) than the similar minimum distance code [[31, 10, 10; 21]] 4 given in Ref. [27].…”

Skew Constacyclic Codes over a Non-Chain Ring

“…Recently entanglement-assisted quantum error-correcting codes (EAQECCs) have been studied vigorously by researchers, see Refs. [ 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ]. Especially, the construction of EAQECCs from LCD codes has been the main focus of attention since the number of pairs of maximally entangled states of an EAQECC derived from an LCD code of length n and dimension k is which give us the occasion to construct EAQECCs with maximal entanglement [ 33 , 38 , 44 ].…”

Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2

“…Several articles have explored the construction of EAQECCs from classical linear codes as binary BCH codes [8,18,21], constacyclic codes [17,27], constacyclic LCD codes [24], cyclic codes [25], generalized Reed-Solomon codes [14,19,20], negacyclic BCH codes [6,7] and algebraic-geometry codes [23]. These papers address particular cases and determine their parameters but no general formula for the parameters of EAQECCs using the previous families of codes is known.…”