Equidistant subspace codes

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• 作者：Elisa Gorla ; ^{elisa.gorla@unine.ch" class="auth_mail" title="E-mail the corresponding author} ; Alberto Ravagnani ^{alberto.ravagnani@unine.ch" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11T71 ; 14G50 ; 94B60 ; 51E23 ; 15A21
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：490
• 期：Complete
• 页码：48-65
• 全文大小：382 K

文摘

In this paper we study equidistant subspace codes, i.e. subspace codes with the property that each two distinct codewords have the same distance. We provide an almost complete classification of such codes, under the assumption that the cardinality of the ground field is large enough. More precisely we prove that, for most values of the parameters, an equidistant code of maximum cardinality is either a sunflower or the orthogonal of a sunflower. We also study equidistant codes with extremal parameters, and establish general properties of equidistant codes that are not sunflowers. Finally, we propose a construction of equidistant codes based on our previous construction of partial spread codes, and provide an efficient decoding algorithm.