New LMRD code bounds for constant dimension codes and improved constructions

D. Heinlein

doi:10.1109/TIT.2019.2905002

New LMRD code bounds for constant dimension codes and improved constructions

D. Heinlein

Department of Communications and Networking

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

We prove upper bounds for the cardinality of constant dimension codes (CDC) which contain a lifted maximum rank distance code (LMRD code) as subset. Thereby we cover all parameters fulfilling k < 3d=2, where k is the codeword dimension and d is the minimum subspace distance. The proofs of the bounds additionally show that an LMRD code L can be unioned with a CDC C (of fitting parameters) without violating the subspace distance condition iff each codeword of C intersects the special subspace of L in at least dimension d=2. This connection is used to find new largest and sometimes bound achieving CDCs for small parameters.

Original language	English
Article number	8667306
Pages (from-to)	4822-4830
Number of pages	9
Journal	IEEE Transactions on Information Theory
Volume	65
Issue number	8
Early online date	2019
DOIs	https://doi.org/10.1109/TIT.2019.2905002
Publication status	Published - 1 Aug 2019
MoE publication type	A1 Journal article-refereed

Keywords

Upper bound
Finite element analysis
Indexes
Extraterrestrial measurements
Encoding
Finite projective spaces
constant dimension codes
subspace codes
subspace distance
rank distance
maximum rank distance codes
lifted maximum rank distance code bound
combinatorics

Access to Document

10.1109/TIT.2019.2905002

Link to publication in Scopus

Projects

1 Finished

Construction and Classification of Discrete Mathematic Structures

Kokkala, J., Laaksonen, A., Heinlein, D., Ganzhinov, M., Östergård, P. & Szollosi, F.

01/09/2015 → 24/09/2019

Project: Academy of Finland: Other research funding

Cite this

Heinlein, D. (2019). New LMRD code bounds for constant dimension codes and improved constructions. IEEE Transactions on Information Theory, 65(8), 4822-4830. [8667306]. https://doi.org/10.1109/TIT.2019.2905002

@article{6cc7aac3ba884f7a99faaecd305d4bee,

title = "New LMRD code bounds for constant dimension codes and improved constructions",

abstract = "We prove upper bounds for the cardinality of constant dimension codes (CDC) which contain a lifted maximum rank distance code (LMRD code) as subset. Thereby we cover all parameters fulfilling k < 3d=2, where k is the codeword dimension and d is the minimum subspace distance. The proofs of the bounds additionally show that an LMRD code L can be unioned with a CDC C (of fitting parameters) without violating the subspace distance condition iff each codeword of C intersects the special subspace of L in at least dimension d=2. This connection is used to find new largest and sometimes bound achieving CDCs for small parameters.",

keywords = "Upper bound, Finite element analysis, Indexes, Extraterrestrial measurements, Encoding, Finite projective spaces, constant dimension codes, subspace codes, subspace distance, rank distance, maximum rank distance codes, lifted maximum rank distance code bound, combinatorics",

author = "D. Heinlein",

year = "2019",

month = aug,

day = "1",

doi = "10.1109/TIT.2019.2905002",

language = "English",

volume = "65",

pages = "4822--4830",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

number = "8",

}

TY - JOUR

T1 - New LMRD code bounds for constant dimension codes and improved constructions

AU - Heinlein, D.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - We prove upper bounds for the cardinality of constant dimension codes (CDC) which contain a lifted maximum rank distance code (LMRD code) as subset. Thereby we cover all parameters fulfilling k < 3d=2, where k is the codeword dimension and d is the minimum subspace distance. The proofs of the bounds additionally show that an LMRD code L can be unioned with a CDC C (of fitting parameters) without violating the subspace distance condition iff each codeword of C intersects the special subspace of L in at least dimension d=2. This connection is used to find new largest and sometimes bound achieving CDCs for small parameters.

AB - We prove upper bounds for the cardinality of constant dimension codes (CDC) which contain a lifted maximum rank distance code (LMRD code) as subset. Thereby we cover all parameters fulfilling k < 3d=2, where k is the codeword dimension and d is the minimum subspace distance. The proofs of the bounds additionally show that an LMRD code L can be unioned with a CDC C (of fitting parameters) without violating the subspace distance condition iff each codeword of C intersects the special subspace of L in at least dimension d=2. This connection is used to find new largest and sometimes bound achieving CDCs for small parameters.

KW - Upper bound

KW - Finite element analysis

KW - Indexes

KW - Extraterrestrial measurements

KW - Encoding

KW - Finite projective spaces

KW - constant dimension codes

KW - subspace codes

KW - subspace distance

KW - rank distance

KW - maximum rank distance codes

KW - lifted maximum rank distance code bound

KW - combinatorics

UR - http://www.scopus.com/inward/record.url?scp=85069478613&partnerID=8YFLogxK

U2 - 10.1109/TIT.2019.2905002

DO - 10.1109/TIT.2019.2905002

M3 - Article

VL - 65

SP - 4822

EP - 4830

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 8

M1 - 8667306

ER -