Maximum Intersection of Linear Codes and Codes Equivalent to Linear

S. V. Avgustinovich; E. V. Gorkunov

doi:10.1134/S1990478919040021

Maximum Intersection of Linear Codes and Codes Equivalent to Linear

S. V. Avgustinovich, E. V. Gorkunov

Section of Discrete Analysis and Operations Research

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

Abstract

We consider linear codes in a space over a finite field with the Hamming metric. A code is called pseudolinear if it is the image of a linear code under an isometric transformation of the space. We derive an upper bound (q - 2)M/q attainable for q ⩾ 3 for the size of the intersection of two different pseudolinear codes of the same size M.

Original language	English
Pages (from-to)	600-605
Number of pages	6
Journal	Journal of Applied and Industrial Mathematics
Volume	13
Issue number	4
DOIs	https://doi.org/10.1134/S1990478919040021
Publication status	Published - 1 Oct 2019

Keywords

code intersection
equivalent code
finite field
isometry
isotopy
linear code
MDS-code
pseudolinear code

Access to Document

10.1134/S1990478919040021

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Maximum Intersection of Linear Codes and Codes Equivalent to Linear'. Together they form a unique fingerprint.

Cite this

@article{c084c1e2f36e48a0a8a8159216598a71,

title = "Maximum Intersection of Linear Codes and Codes Equivalent to Linear",

abstract = "We consider linear codes in a space over a finite field with the Hamming metric. A code is called pseudolinear if it is the image of a linear code under an isometric transformation of the space. We derive an upper bound (q - 2)M/q attainable for q ⩾ 3 for the size of the intersection of two different pseudolinear codes of the same size M.",

keywords = "code intersection, equivalent code, finite field, isometry, isotopy, linear code, MDS-code, pseudolinear code",

author = "Avgustinovich, {S. V.} and Gorkunov, {E. V.}",

year = "2019",

month = oct,

day = "1",

doi = "10.1134/S1990478919040021",

language = "English",

volume = "13",

pages = "600--605",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "4",

}

TY - JOUR

T1 - Maximum Intersection of Linear Codes and Codes Equivalent to Linear

AU - Avgustinovich, S. V.

AU - Gorkunov, E. V.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - We consider linear codes in a space over a finite field with the Hamming metric. A code is called pseudolinear if it is the image of a linear code under an isometric transformation of the space. We derive an upper bound (q - 2)M/q attainable for q ⩾ 3 for the size of the intersection of two different pseudolinear codes of the same size M.

AB - We consider linear codes in a space over a finite field with the Hamming metric. A code is called pseudolinear if it is the image of a linear code under an isometric transformation of the space. We derive an upper bound (q - 2)M/q attainable for q ⩾ 3 for the size of the intersection of two different pseudolinear codes of the same size M.

KW - code intersection

KW - equivalent code

KW - finite field

KW - isometry

KW - isotopy

KW - linear code

KW - MDS-code

KW - pseudolinear code

UR - http://www.scopus.com/inward/record.url?scp=85078933345&partnerID=8YFLogxK

U2 - 10.1134/S1990478919040021

DO - 10.1134/S1990478919040021

M3 - Article

AN - SCOPUS:85078933345

VL - 13

SP - 600

EP - 605

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -