Flag codes from planar spreads in network coding

被引：14

作者：

Alonso-Gonzalez, Clementa ^{[1
]}

Angel Navarro-Perez, Miguel ^{[1
]}

Soler-Escriva, Xaro ^{[1
]}

机构：

[1] Univ dAlacant, Dept Matemat, Ap Correus 99, E-03080 Alacant, Spain

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2020年 / 68卷

关键词：

Network coding; Subspace codes; Projective space; Spreads; Flag codes;

D O I：

10.1016/j.ffa.2020.101745

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a class of multishot network codes given by families of nested subspaces (flags) of a vector space F-q(n), being q a prime power and F-q the finite field of q elements. In particular, we focus on flag codes having maximum distance (optimum distance flag codes). We explore the existence of these codes from spreads, based on the good properties of the latter ones. For n = 2k, we show that optimum distance full flag codes with the largest size are exactly those that can be constructed from a planar spread. We give a precise construction of them as well as a decoding algorithm. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：20

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