Maximum distance separable poset codes

被引：32
|
作者：
Hyun, Jong Yoon [1 ]
Kim, Hyun Kwang [1 ]
机构：
[1] Pohang Univ Sci & Technol, Dept Math, Pohang 790784, South Korea
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2008年 / 48卷 / 03期
关键词：
maximum distance separable code; poset code; discrete Poisson summation formula; Moebius inversion formula;
D O I：
10.1007/s10623-008-9204-8
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We derive the Singleton bound for poset codes and define the MDS poset codes as linear codes which attain the Singleton bound. In this paper, we study the basic properties of MDS poset codes. First, we introduce the concept of I-perfect codes and describe the MDS poset codes in terms of I -perfect codes. Next, we study the weight distribution of an MDS poset code and show that the weight distribution of an MDS poset code is completely determined. Finally, we prove the duality theorem which states that a linear code C is an MDS P-code if and only if C-perpendicular to is an MDS (P) over tilde -code, where C-perpendicular to is the dual code of C and (P) over tilde is the dual poset of P.
引用
收藏
页码：247 / 261
页数：15
相关论文
共 50 条
12345