The geometric approach to the existence of some quaternary Griesmer codes

被引：1

作者：

Rousseva, Assia ^{[1
]}

Landjev, Ivan ^{[2
,3
]}

机构：

[1] Sofia Univ St Kl Ohridski, Fac Math & Informat, 5 J Bourchier Blvd, Sofia 1164, Bulgaria

[2] New Bulgarian Univ, 21 Montevideo Str, Sofia 1618, Bulgaria

[3] Bulgarian Acad Sci, Inst Math & Informat, 8 Acad G Bonchev Str, Sofia 1113, Bulgaria

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2020年 / 88卷 / 09期

关键词：

Linear codes; Griesmer bound; Griesmer codes; Griesmer arcs; Finite projective geometries; Optimal linear codes; LINEAR CODES; EXTENSION THEOREM; NONEXISTENCE;

D O I：

10.1007/s10623-020-00777-0

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we prove the nonexistence of the hypothetical arcs with parameters (395, 100), (396, 100), (448, 113), and (449, 113) in PG(4, 4). This rules out the existence of Giesmer codes with parameters [395, 5, 295](4), [396, 5, 296](4), [448, 5, 335](4), [449, 5, 336](4) and solves four instances of the main problem of coding theory for q = 4, k = 5. The proof relies on the characterization of (100, 26)- and (113, 29)-arcs in PG(3, 4) and is entirely computer-free.

引用

页码：1925 / 1940

页数：16

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