Entanglement-assisted quantum codes from arbitrary binary linear codes

Qian, Jianfa; Zhang, Lína

doi:10.1007/s10623-014-9997-6

Cited by 50 publications

(13 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Qian and Zhang [15] used binary LCD codes which are transitive to prove the existence of an asymptotically good family of EAQECCs [17]. We prove in this section that the same arguments are valid for finite fields of odd characteristic.…”

Section: Asymptotically Good Eaqeccsmentioning

confidence: 80%

Constructions of good entanglement-assisted quantum error correcting codes

Guenda

Jitman

Gulliver

2017

Des. Codes Cryptogr.

208

104

View full text Add to dashboard Cite

Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and fundamental class of codes. They allow for the construction of quantum codes from classical codes by relaxing the duality condition and using pre-shared entanglement between the sender and receiver. However, in general it is not easy to determine the number of shared pairs required to construct an EAQECC. In this paper, we show that this number is related to the hull of the classical code. Using this fact, we give methods to construct EAQECCs requiring desirable amount of entanglement. This leads to design families of EAQECCs with good error performance. Moreover, we construct maximal entanglement EAQECCs from LCD codes. Finally, we prove the existence of asymptotically good EAQECCs in the odd characteristic case. * K. Guenda is with the Faculty

show abstract

Section: Asymptotically Good Eaqeccsmentioning

confidence: 80%

Constructions of good entanglement-assisted quantum error correcting codes

Guenda

Jitman

Gulliver

2017

Des. Codes Cryptogr.

208

104

View full text Add to dashboard Cite

show abstract

“…The application of LCD codes in constructing good EAQECCs has aroused the interest of researchers in the past few years, and many classes of maximal entanglement EAQECCs have been constructed (see [10,18,23,24]).…”

Section: Introductionmentioning

confidence: 99%

Hermitian LCD codes over $\mathbb {F}_{q^{2}}+u \mathbb {F}_{q^{2}}$ and their applications to maximal entanglement EAQECCs

2021

Cryptogr. Commun.

View full text Add to dashboard Cite

Let R = F q 2 + uF q 2 , where F q 2 is the finite field with q 2 elements, q is a power of a prime p, and u 2 = 0. In this paper, a class of maximal entanglement entanglement-assisted quantum error-correcting codes (EAQECCs) is obtained by employing (1 − u)-constacyclic Hermitian linear complementary dual (LCD) codes of length n over R. First, we give a sufficient condition for a linear code C of length n over R to be a Hermitian LCD code and claim that there does not exist a non-free Hermitian LCD code of length n over R. Also, assume that gcd(n, q) = 1, and γ is a unit in R, we obtain all γ -constacyclic Hermitian LCD codes. Finally, we derive symplectic LCD codes of length 2n over F q 2 as Gray images of linear and constacyclic codes of length n over R. By using the explicit symplectic method in [9], we get the desired maximal entanglement EAQECCs.

show abstract

“…The study of error correction coding is based on the practical requirements of modern digital communication technology, and the profound involvement of various mathematical theories promotes the development and prosperity of this area of researches. Now, error-correcting coding theory has been applied to construct authentication codes, quantum error-correcting codes and post-quantum cryptography ( [15], [23], [27], [32], [33], [39], [43], [50], [59]). The problems arising in these fields have put forward various new requirements and subjects for the development of coding theory.…”

Section: Introductionmentioning

confidence: 99%

Explicit Representation and Enumeration of Repeated-Root (δ + αu²)-Constacyclic Codes Over F₂^m[u]/‹u ^2λ›

et al. 2020

View full text Add to dashboard Cite

Let F 2 m be a finite field of 2 m elements, λ and k be integers satisfying λ, k ≥ 2 and denote R = F 2 m [u]/ u 2λ. Let δ, α ∈ F × 2 m. For any odd positive integer n, we give an explicit representation and enumeration for all distinct (δ + αu 2)-constacyclic codes over R of length 2 k n, and provide a clear formula to count the number of all these codes. In particular, we conclude that every (δ + αu 2)-constacyclic code over R of length 2 k n is an ideal generated by at most 2 polynomials in the ring R[x]/ x 2 k n − (δ + αu 2). As an example, we listed all 135 distinct (1 + u 2)-constacyclic codes of length 4 over F 2 [u] u 4 , and apply our results to determine all 11 self-dual codes among them. INDEX TERMS Type 2 constacyclic code, linear code, repeated-root code, finite chain ring.

show abstract

Entanglement-assisted quantum codes from arbitrary binary linear codes

Cited by 50 publications

References 26 publications

Constructions of good entanglement-assisted quantum error correcting codes

Constructions of good entanglement-assisted quantum error correcting codes

Hermitian LCD codes over $\mathbb {F}_{q^{2}}+u \mathbb {F}_{q^{2}}$ and their applications to maximal entanglement EAQECCs

Explicit Representation and Enumeration of Repeated-Root (δ + αu²)-Constacyclic Codes Over F₂^m[u]/‹u ^2λ›

Contact Info

Product

Resources

About

Entanglement-assisted quantum codes from arbitrary binary linear codes

Cited by 50 publications

References 26 publications

Constructions of good entanglement-assisted quantum error correcting codes

Constructions of good entanglement-assisted quantum error correcting codes

Hermitian LCD codes over $\mathbb {F}_{q^{2}}+u \mathbb {F}_{q^{2}}$ and their applications to maximal entanglement EAQECCs

Explicit Representation and Enumeration of Repeated-Root (δ + αu²)-Constacyclic Codes Over F₂ m [u]/‹u 2λ›

Contact Info

Product

Resources

About

Explicit Representation and Enumeration of Repeated-Root (δ + αu²)-Constacyclic Codes Over F₂^m[u]/‹u ^2λ›