On the 3-extendability of quaternary linear codes

被引：1

作者：

Kanda, H. ^{[1
]}

Maruta, T. ^{[1
]}

机构：

[1] Osaka Prefecture Univ, Dept Math Sci, Sakai, Osaka 5998531, Japan

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2018年 / 52卷

关键词：

Linear codes; Extension; Finite projective spaces; Odd sets; EXTENSION THEOREM; EXTENDABILITY; GCD(D;

D O I：

10.1016/j.ffa.2018.04.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the extendability of linear codes over F-4, the field of order four. Let C be [n, k, d](4) code with d equivalent to 1 (mod 4), k >= 3. The weight spectrum modulo 4 (4 -WS) of C is defined as the ordered 4-tuple (w(0), w(1), w(2), W-3) with w(0) = 1/3 Sigma 4|i>0 A(i), w(j) = 1/3 Sigma i equivalent to j (mod 4) A(i) for j = 1, 2, 3. We prove that C is 3-extendable if w(0) + w(2) = theta(k-2) and if either (a) w(1) - w(0) < 4(k-2) + 4 theta(k-3); (b) w(1) - w(c) > 10 . 4(k-3) - theta(k-3) or (c) (w(0), w(1)) = (theta(k-3), 6 . 4(k-3)). We also give a sufficient condition for the l-extendability of [n, k, d](4) codes with d equivalent to 4 - l (mod 4), k >= 3 for l = 1, 2, 3 when w(0) + W-2 = theta(k-2) + 2 . 4(k-2). (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：126 / 136

页数：11

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