We study locally recoverable codes on algebraic curves. In the first part of the manuscript, we provide a bound on the generalized Hamming weight of these codes. In the second part, we propose a new family of algebraic geometric LRC codes, which are LRC codes from the Norm-Trace curve. Finally, using some properties of Hermitian codes, we improve the bounds on the distance proposed in Barg et al. (2015) [1] of some Hermitian LRC codes. © 2016 Elsevier Inc. All rights reserved.
Higher Hamming weights for locally recoverable codes on algebraic curves / Ballico, Edoardo; Marcolla, Chiara. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - STAMPA. - 40:(2016), pp. 61-72. [10.1016/j.ffa.2016.03.004]
Higher Hamming weights for locally recoverable codes on algebraic curves
Ballico, Edoardo;Marcolla, Chiara
2016-01-01
Abstract
We study locally recoverable codes on algebraic curves. In the first part of the manuscript, we provide a bound on the generalized Hamming weight of these codes. In the second part, we propose a new family of algebraic geometric LRC codes, which are LRC codes from the Norm-Trace curve. Finally, using some properties of Hermitian codes, we improve the bounds on the distance proposed in Barg et al. (2015) [1] of some Hermitian LRC codes. © 2016 Elsevier Inc. All rights reserved.| File | Dimensione | Formato | |
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