Generalizing Subspace Codes to Flag Codes Using Group Actions

Dirk Liebhold; Gabriele Nebe; María Ángeles Vázquez-Castro

doi:10.1007/978-3-319-70293-3_4

Generalizing Subspace Codes to Flag Codes Using Group Actions

Dirk Liebhold, Gabriele Nebe, María Ángeles Vázquez-Castro

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Abstract

© 2018, Springer International Publishing AG. In this chapter, we first discuss structural properties of subspace codes by applying group actions. We will see that the projective space, the Grassmannian and the Schubert cells can be realized by looking at the orbits of certain linear groups on matrices. The approach naturally leads to a generalization, where we replace subspace codes with flag codes. We describe and analyze a channel model for these new codes that is similar to the operator channel introduced by Koetter and Kschischang, give examples of flag codes and discuss how to compute sphere packing and sphere covering bounds for flag codes.

Original language	English
Title of host publication	Signals and Communication Technology
Pages	67-89
Number of pages	22
ISBN (Electronic)	1860-4870
DOIs	https://doi.org/10.1007/978-3-319-70293-3_4
Publication status	Published - 1 Jan 2018

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title = "Generalizing Subspace Codes to Flag Codes Using Group Actions",

abstract = "{\textcopyright} 2018, Springer International Publishing AG. In this chapter, we first discuss structural properties of subspace codes by applying group actions. We will see that the projective space, the Grassmannian and the Schubert cells can be realized by looking at the orbits of certain linear groups on matrices. The approach naturally leads to a generalization, where we replace subspace codes with flag codes. We describe and analyze a channel model for these new codes that is similar to the operator channel introduced by Koetter and Kschischang, give examples of flag codes and discuss how to compute sphere packing and sphere covering bounds for flag codes.",

author = "Dirk Liebhold and Gabriele Nebe and V{\'a}zquez-Castro, {Mar{\'i}a {\'A}ngeles}",

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AU - Nebe, Gabriele

AU - Vázquez-Castro, María Ángeles

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Y1 - 2018/1/1

N2 - © 2018, Springer International Publishing AG. In this chapter, we first discuss structural properties of subspace codes by applying group actions. We will see that the projective space, the Grassmannian and the Schubert cells can be realized by looking at the orbits of certain linear groups on matrices. The approach naturally leads to a generalization, where we replace subspace codes with flag codes. We describe and analyze a channel model for these new codes that is similar to the operator channel introduced by Koetter and Kschischang, give examples of flag codes and discuss how to compute sphere packing and sphere covering bounds for flag codes.

AB - © 2018, Springer International Publishing AG. In this chapter, we first discuss structural properties of subspace codes by applying group actions. We will see that the projective space, the Grassmannian and the Schubert cells can be realized by looking at the orbits of certain linear groups on matrices. The approach naturally leads to a generalization, where we replace subspace codes with flag codes. We describe and analyze a channel model for these new codes that is similar to the operator channel introduced by Koetter and Kschischang, give examples of flag codes and discuss how to compute sphere packing and sphere covering bounds for flag codes.

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DO - 10.1007/978-3-319-70293-3_4

M3 - Chapter

SN - 1860-4862

SP - 67

EP - 89

BT - Signals and Communication Technology

ER -

Generalizing Subspace Codes to Flag Codes Using Group Actions

Abstract

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