BINARY SUBSPACE CODES IN SMALL AMBIENT SPACES

Daniel Heinlein; Sascha Kurz

doi:10.3934/amc.2018048

BINARY SUBSPACE CODES IN SMALL AMBIENT SPACES

Daniel Heinlein^*
, Sascha Kurz

^*Tämän työn vastaava kirjoittaja

University of Bayreuth

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

2 Sitaatiot (Scopus)

Abstrakti

Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for projective dimensions of at most 7, i.e., affine dimensions of at most 8. We obtain several improvements of the bounds and perform two classifications of optimal subspace codes, which are unknown so far in the literature.

Alkuperäiskieli	Englanti
Sivut	817-839
Sivumäärä	23
Julkaisu	Advances in Mathematics of Communications
Vuosikerta	12
Numero	4
DOI - pysyväislinkit	https://doi.org/10.3934/amc.2018048
Tila	Julkaistu - marrask. 2018
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Rahoitus

The authors were supported by the DFG project "Ganzzahlige Optimierungsmodelle fur Subspace Codes und endliche Geometrie" (DFG grants KU 2430/3-1, WA 1666/9-1).

Pääsy asiakirjaan

10.3934/amc.2018048

Siteeraa tätä

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title = "BINARY SUBSPACE CODES IN SMALL AMBIENT SPACES",

abstract = "Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for projective dimensions of at most 7, i.e., affine dimensions of at most 8. We obtain several improvements of the bounds and perform two classifications of optimal subspace codes, which are unknown so far in the literature.",

keywords = "Galois geometry, network coding, subspace code, partial spread, NETWORK ERROR-CORRECTION, CODING THEORY, LOWER BOUNDS, DIMENSION, DISTANCE, DESIGNS",

author = "Daniel Heinlein and Sascha Kurz",

year = "2018",

month = nov,

doi = "10.3934/amc.2018048",

language = "English",

volume = "12",

pages = "817--839",

journal = "Advances in Mathematics of Communications",

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publisher = "American Institute of Mathematical Sciences",

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T1 - BINARY SUBSPACE CODES IN SMALL AMBIENT SPACES

AU - Heinlein, Daniel

AU - Kurz, Sascha

PY - 2018/11

Y1 - 2018/11

N2 - Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for projective dimensions of at most 7, i.e., affine dimensions of at most 8. We obtain several improvements of the bounds and perform two classifications of optimal subspace codes, which are unknown so far in the literature.

AB - Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for projective dimensions of at most 7, i.e., affine dimensions of at most 8. We obtain several improvements of the bounds and perform two classifications of optimal subspace codes, which are unknown so far in the literature.

KW - Galois geometry

KW - network coding

KW - subspace code

KW - partial spread

KW - NETWORK ERROR-CORRECTION

KW - CODING THEORY

KW - LOWER BOUNDS

KW - DIMENSION

KW - DISTANCE

KW - DESIGNS

U2 - 10.3934/amc.2018048

DO - 10.3934/amc.2018048

M3 - Article

SN - 1930-5346

VL - 12

SP - 817

EP - 839

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

IS - 4

ER -

BINARY SUBSPACE CODES IN SMALL AMBIENT SPACES

Abstrakti

Rahoitus

Pääsy asiakirjaan

Sormenjälki

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