Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/145509
Title: Repairing algebraic geometry codes
Authors: Jin, Lingfei
Luo, Yuan
Xing, Chaoping
Keywords: Engineering::Computer science and engineering
Issue Date: 2018
Source: Jin, L., Luo, Y., & Xing, C. (2018). Repairing algebraic geometry codes. IEEE Transactions on Information Theory, 64(2), 900-908. doi:10.1109/TIT.2017.2773089
Journal: IEEE Transactions on Information Theory
Abstract: Minimum storage regenerating codes have minimum storage of data in each node and therefore are maximal distance separable (for short) codes. Thus, the number of nodes is upper-bounded by 2 b , where ú is the bits of data stored in each node. From both theoretical and practical points of view (see the details in Section 1), it is natural to consider regenerating codes that nearly have minimum storage of data, and meanwhile, the number of nodes is unbounded. One of the candidates for such regenerating codes is an algebraic geometry code. In this paper, we generalize the repairing algorithm of Reed-Solomon codes given by Guruswami and Wotters to algebraic geometry codes and present a repairing algorithm for arbitrary one-point algebraic geometry codes. By applying our repairing algorithm to the one-point algebraic geometry codes based on the Garcia- Stichtenoth tower, one can repair a code of rate 1 - e and length n over F q with bandwidth (n - 1)(1 - τ) log q for any e = 2 (τ-1/2) logq with a real τ ∈ (0, 1/2). In addition, storage in each node for an algebraic geometry code is close to the minimum storage. Due to nice structures of Hermitian curves, repairing of Hermitian codes is also investigated. As a result, we are able to show that algebraic geometry codes are regenerating codes with good parameters.
URI: https://hdl.handle.net/10356/145509
ISSN: 1557-9654
DOI: 10.1109/TIT.2017.2773089
Rights: © 2017 Institute of Electrical and Electronics Engineers (IEEE). All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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