Higher Hamming weights for locally recoverable codes on algebraic curves

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• 作者：Edoardo Ballico¹ ; ^{ballico@science.unitn.it" class="auth_mail" title="E-mail the corresponding author} ; Chiara Marcolla ; ^{chiara.marcolla@unito.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11G20 ; secondary ; 11T71 ; 14H51 ; 14H50
• 刊名：Finite Fields and Their Applications
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：40
• 期：Complete
• 页码：61-72
• 全文大小：340 K

文摘

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.