Cyclic subspace codes and sidon spaces

Netanel Raviv, Itzhak Tamo

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

The interest in subspace codes has increased in recent years due to their application in error correction for random network coding. In order to study their properties and find good constructions, the notion of cyclic subspace codes was introduced by using the extension field structure of the ambient space. However, to this date there exists no general construction with a polynomial relation between k, the dimension of the codewords, and n, the dimension of the entire space. Independently of the study of cyclic subspace codes, sSidon spaces were recently introduced by Bachoc et al. as a tool for the study of certain multiplicative properties of subspaces over finite fields. In this paper it is shown that Sidon spaces are necessary and sufficient for obtaining a full-orbit cyclic subspace code with minimum distance 2 k - 2. By presenting several constructions of Sidon spaces, full-orbit cyclic subspace codes are obtained, in which n is quadratic in k. The constructions are based on a variety of tools; namely, Sidon sets, that are sets of integers in which all pairwise sums are distinct, irreducible polynomials, and linearized polynomials. Further, the existence of a Sidon space in which n is linear in k is shown, alongside the fact that any Sidon space induces a Sidon set.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages784-788
Number of pages5
ISBN (Electronic)9781509040964
DOIs
StatePublished - 9 Aug 2017
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/TerritoryGermany
CityAachen
Period25/06/1730/06/17

Funding

FundersFunder number
NSF-BSF2015814
Israel Science Foundation1030/15

    Keywords

    • Cyclic subspace codes
    • Linearized polynomials
    • Network Coding
    • Sidon sets
    • Sidon spaces

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