메뉴 건너뛰기
Library Notice
Institutional Access
If you certify, you can access the articles for free.
Check out your institutions.
ex)Hankuk University, Nuri Motors
Log in Register Help KOR
Subject
Humanities
General Humanities History Philosophy Religious Studies Linguistics and Literature Other Humanities
Social science
General Social Science Business Management Tourism Education Military Science Library and Information Science Law Sociology Journalism and Media Studies Psychological Science Political Science and Diplomacy Geography Public Administration Economics International Trade Anthropology Other Social Science
Natural science
General Natural Science Physics Biology Life Sciences Mathematics/Statistics Astronomy Earth Science Chemistry Other Natural Science
Engineering
General Engineering Architectural Engineering Mechanical Engineering Industrial Engineering Material/Energy Engineering Electrical and Electronic Engineering Marine and Ocean Engineering Chemical Engineering Computer Science Other Engineering
Medical science
General Medical Science Nursing Science Veterinary Pharmacy Traditional Korean Medicine Basic Medicine Clinical Medicine Other Medicine
Agriculture and Fishery
General Agriculture and Fishery Agriculture Fishery Science Food Science Forestry Animal Husbandry Marine Transportation Studies Other Agriculture and Fishery
Art and Kinesiology
General Arts Design Fine Arts Cosmetology Photography Music Fashion Kinesiology Performing Media Arts Other Arts and Kinesiology
Interdisciplinary Studies
Interdisciplinary Research Science and Technology Studies Brain and Cognitive Science Technology Policy Other Interdisciplinary Studies

KOR

A construction of two-weight codes and its applications
Recommendations
Search

논문 기본 정보

Type
Academic journal
Author
Journal
대한수학회 대한수학회보 대한수학회보 제54권 제3호 KCI Accredited Journals
Published
2017.1
Pages
731 - 736 (6page)

Usage

cover
A construction of two-weight codes and its applications
Ask AI
Recommendations
Search

Abstract· Keywords

Report Errors
It is well-known that there exists a constant-weight $[s \theta_{k-1},k, $ $ sq^{k-1}]_q$ code for any positive integer $s$, which is an $s$-fold simplex code, where $\theta_{j}=(q^{j+1}-1)/(q-1)$. This gives an upper bound $n_q(k, s q^{k-1}+d) \le s \theta_{k-1} + n_q(k,d)$ for any positive integer $d$, where $n_q(k,d)$ is the minimum length $n$ for which an $[n,k,d]_q$ code exists. We construct a two-weight $[s \theta_{k-1}+1,k, s q^{k-1}]_q$ code for $1 \le s \le k-3$, which gives a better upper bound $n_q(k, s q^{k-1}+d) \le s \theta_{k-1} +1 + n_q(k-1,d)$ for $1 \le d \le q^s$. As another application, we prove that $n_q(5,d)=\sum_{i=0}^{4}{\left\lceil{{d}/{q^i}}\right\rceil}$ for $q^{4}+1 \le d \le q^4+q$ for any prime power $q$.
#linear code #two-weight code #length optimal code #Griesmer bound #projective space

Contents

No content found

References (10)

Add References
F. J. MacWilliams / 1977 / The Theory of Error-Correcting Codes / North-Holland google schola G. Solomon / 1965 / Algebraically punctured cyclic codes / Inform. and Control 8 (2) : 170 ~ 179 google schola J. H. Griesmer / 1960 / A bound for error-correcting codes / IBM J. Res. Develop 4 : 532 ~ 542 google schola J. W. P. Hirschfeld / 1998 / Projective Geometries over Finite Fields / Clarendon Press google schola R. Calderbank / 1986 / The geometry of two-weight codes / Bull. London Math. Soc 18 (2) : 97 ~ 122 google schola

Recommendations

It is an article recommended by DBpia according to the article similarity. Check out the related articles!

Related Authors

Recently viewed articles

Suicidal ideation among firefighters: A systematic literature review
Ung Il Kang, Jung Eun-Kyungundefined2023.04
 A Study on the Code Rate Change of Topological Quantum Error Correction Code
Hyunwoo Jung, Jeongseok HaKorea Institute Of Communication Sciences2021.02
 Medical Malpractice and Civil Liability of Nurse
Yang JaeMoHan Yang Law Association2008.06
 A Review on the Family Policy of a Local Government from “Democratic Caring” : A Case Study of Seoul City
Song, Dayoung, Jang 외 3명Keimyung University Institute for Women's Studies2017.06

Comments(0)

0

Write first comments.