Distance Distributions of Cyclic Orbit Codes

Heide Gluesing-Luerssen, Hunter Lehmann

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The distance distribution of a code is the vector whose ith entry is the number of pairs of codewords with distance i. We investigate the structure of the distance distribution for cyclic orbit codes, which are subspace codes generated by the action of Fqn∗ on an Fq-subspace U of Fqn. Note that Fqn∗ is a Singer cycle in the general linear group of all Fq-automorphisms of Fqn. We show that for full-length orbit codes with maximal possible distance the distance distribution depends only on q,n, and the dimension of U. For full-length orbit codes with lower minimum distance, we provide partial results towards a characterization of the distance distribution, especially in the case that any two codewords intersect in a space of dimension at most 2. Finally, we briefly address the distance distribution of a union of full-length orbit codes with maximum distance.

Original languageEnglish
Pages (from-to)447-470
Number of pages24
JournalDesigns, Codes, and Cryptography
Volume89
Issue number3
DOIs
StatePublished - Mar 2021

Bibliographical note

Funding Information:
HGL was partially supported by the Grant #422479 from the Simons Foundation.

Publisher Copyright:
© 2021, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Coding theory
  • Cyclic orbit codes
  • Subspace codes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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