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Vol. 46 No. 3 (2020)
Serdica Mathematical Journal

Articles

The non-existence of [383, 5, 286] and [447, 5, 334] quaternary linear codes

Published 18-06-2021

  • Hitoshi Kanda

Hitoshi Kanda
Osaka Prefecture University

Abstract

It is known that \(n_4(5,286) = 383\) or 384 and \(n_4(5,334) = 447\) or 448, where \(n_q(k,d)\) is the minimum length \(n\) for which an \([n,k,d]_q\) code exists. We prove the non-existence of \([383,5,286]_4\) and \([447,5,334]_4\) codes, which determine the exact value of \(n_4(5,d)\) for \(d = 286, 334\).

2020 Mathematics Subject Classification:

94B27, 94B65, 94B05

Keywords

optimal linear code, Griesmer bound, geometric method, quaternary linear code

Full text

Author Details

Hitoshi Kanda

Department of Mathematical Sciences
Osaka Prefecture University
Sakai, Osaka 599-8531, Japan
e-mail: jinza80kirisame@gmail.com

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