New and updated semidefinite programming bounds for subspace codes

Daniel Heinlein; Ferdinand Ihringer

doi:10.3934/amc.2020034

New and updated semidefinite programming bounds for subspace codes

Daniel Heinlein^*, Ferdinand Ihringer

^*Tämän työn vastaava kirjoittaja

Information Theory

Ghent University

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

Abstrakti

We show that A₂ (7, 4) ≤ 388 and, more generally, A_q(7, 4) ≤ (q² − q + 1)[7] + q⁴ − 2q³ + 3q² − 4q + 4 by semidefinite programming for q ≤ 101. Furthermore, we extend results by Bachoc et al. on SDP bounds for A₂ (n, d), where d is odd and n is small, to A_q(n, d) for small q and small n.

Alkuperäiskieli	Englanti
Sivut	613-630
Sivumäärä	18
Julkaisu	Advances in Mathematics of Communications
Vuosikerta	14
Numero	4
Varhainen verkossa julkaisun päivämäärä	marrask. 2019
DOI - pysyväislinkit	https://doi.org/10.3934/amc.2020034
Tila	Julkaistu - marrask. 2020
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Pääsy asiakirjaan

10.3934/amc.2020034

Muut tiedostot ja linkit

Link to publication in Scopus

Konstruktion och klassificering av diskreta matematiska strukturer
Östergård, P. (Vastuullinen tutkija)
01/09/2015 → 31/08/2019
Projekti: Academy of Finland: Other research funding

Siteeraa tätä

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title = "New and updated semidefinite programming bounds for subspace codes",

abstract = "We show that A2 (7, 4) ≤ 388 and, more generally, Aq(7, 4) ≤ (q2 − q + 1)[7] + q4 − 2q3 + 3q2 − 4q + 4 by semidefinite programming for q ≤ 101. Furthermore, we extend results by Bachoc et al. on SDP bounds for A2 (n, d), where d is odd and n is small, to Aq(n, d) for small q and small n.",

keywords = "Coherent configuration, Finite projective space, Network coding, Semidefinite programming, Subspace code, Subspace distance",

author = "Daniel Heinlein and Ferdinand Ihringer",

year = "2020",

month = nov,

doi = "10.3934/amc.2020034",

language = "English",

volume = "14",

pages = "613--630",

journal = "Advances in Mathematics of Communications",

issn = "1930-5346",

publisher = "American Institute of Mathematical Sciences",

number = "4",

}

TY - JOUR

T1 - New and updated semidefinite programming bounds for subspace codes

AU - Heinlein, Daniel

AU - Ihringer, Ferdinand

PY - 2020/11

Y1 - 2020/11

N2 - We show that A2 (7, 4) ≤ 388 and, more generally, Aq(7, 4) ≤ (q2 − q + 1)[7] + q4 − 2q3 + 3q2 − 4q + 4 by semidefinite programming for q ≤ 101. Furthermore, we extend results by Bachoc et al. on SDP bounds for A2 (n, d), where d is odd and n is small, to Aq(n, d) for small q and small n.

AB - We show that A2 (7, 4) ≤ 388 and, more generally, Aq(7, 4) ≤ (q2 − q + 1)[7] + q4 − 2q3 + 3q2 − 4q + 4 by semidefinite programming for q ≤ 101. Furthermore, we extend results by Bachoc et al. on SDP bounds for A2 (n, d), where d is odd and n is small, to Aq(n, d) for small q and small n.

KW - Coherent configuration

KW - Finite projective space

KW - Network coding

KW - Semidefinite programming

KW - Subspace code

KW - Subspace distance

UR - http://www.scopus.com/inward/record.url?scp=85092411204&partnerID=8YFLogxK

U2 - 10.3934/amc.2020034

DO - 10.3934/amc.2020034

M3 - Article

AN - SCOPUS:85092411204

SN - 1930-5346

VL - 14

SP - 613

EP - 630

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

IS - 4

ER -

New and updated semidefinite programming bounds for subspace codes

Abstrakti

Pääsy asiakirjaan

Muut tiedostot ja linkit

Sormenjälki

Projektit

Konstruktion och klassificering av diskreta matematiska strukturer

Siteeraa tätä