Note on an Improvement of the Griesmer Bound for q-ary Linear Codes

Hamada, Noboru; Maruta, Tatsuya

Serdica Journal of Computing (2011)

  • Volume: 5, Issue: 3, page 199-206
  • ISSN: 1312-6555

Abstract

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Let nq(k, d) denote the smallest value of n for which an [n, k, d]q code exists for given integers k and d with k ≥ 3, 1 ≤ d ≤ q^(k−1) and a prime or a prime power q. The purpose of this note is to show that there exists a series of the functions h3,q, h4,q, ..., hk,q such that nq(k, d) can be expressed.This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 20540129.

How to cite

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Hamada, Noboru, and Maruta, Tatsuya. "Note on an Improvement of the Griesmer Bound for q-ary Linear Codes." Serdica Journal of Computing 5.3 (2011): 199-206. <http://eudml.org/doc/219598>.

@article{Hamada2011,
abstract = {Let nq(k, d) denote the smallest value of n for which an [n, k, d]q code exists for given integers k and d with k ≥ 3, 1 ≤ d ≤ q^(k−1) and a prime or a prime power q. The purpose of this note is to show that there exists a series of the functions h3,q, h4,q, ..., hk,q such that nq(k, d) can be expressed.This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 20540129.},
author = {Hamada, Noboru, Maruta, Tatsuya},
journal = {Serdica Journal of Computing},
keywords = {Linear Codes; Griesmer Bound; Griesmer bound; -ary linear codes},
language = {eng},
number = {3},
pages = {199-206},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Note on an Improvement of the Griesmer Bound for q-ary Linear Codes},
url = {http://eudml.org/doc/219598},
volume = {5},
year = {2011},
}

TY - JOUR
AU - Hamada, Noboru
AU - Maruta, Tatsuya
TI - Note on an Improvement of the Griesmer Bound for q-ary Linear Codes
JO - Serdica Journal of Computing
PY - 2011
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 5
IS - 3
SP - 199
EP - 206
AB - Let nq(k, d) denote the smallest value of n for which an [n, k, d]q code exists for given integers k and d with k ≥ 3, 1 ≤ d ≤ q^(k−1) and a prime or a prime power q. The purpose of this note is to show that there exists a series of the functions h3,q, h4,q, ..., hk,q such that nq(k, d) can be expressed.This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 20540129.
LA - eng
KW - Linear Codes; Griesmer Bound; Griesmer bound; -ary linear codes
UR - http://eudml.org/doc/219598
ER -

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