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Computer Science > Information Theory

arXiv:1812.09019 (cs)
[Submitted on 21 Dec 2018 (v1), last revised 6 Dec 2019 (this version, v4)]

Title:Euclidean and Hermitian Hulls of MDS Codes and Their Applications to EAQECCs

Authors:Weijun Fang, Fang-Wei Fu, Lanqiang Li, Shixin Zhu
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Abstract:In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can determine the dimensions of their Euclidean hulls or Hermitian hulls. It turns out that the dimensions of Euclidean hulls or Hermitian hulls of the codes in our constructions can take all or almost all possible values. As a consequence, we can apply our results to entanglement-assisted quantum error-correcting codes (EAQECCs) and obtain several new families of MDS EAQECCs with flexible parameters. The required number of maximally entangled states of these MDS EAQECCs can take all or almost all possible values. Moreover, several new classes of q-ary MDS EAQECCs of length n > q + 1 are also obtained.
Comments: Accepted for publication in IEEE Transactions on Information Theory
Subjects: Information Theory (cs.IT)
Cite as: arXiv:1812.09019 [cs.IT]
  (or arXiv:1812.09019v4 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.1812.09019
Related DOI: https://doi.org/10.1109/TIT.2019.2950245

Submission history

From: Lanqiang Li [view email]
[v1] Fri, 21 Dec 2018 09:43:25 UTC (15 KB)
[v2] Wed, 2 Jan 2019 07:24:45 UTC (13 KB)
[v3] Fri, 4 Jan 2019 08:09:27 UTC (13 KB)
[v4] Fri, 6 Dec 2019 03:36:20 UTC (17 KB)
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Shixin Zhu
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