Maximum distance separable poset codes

  • Authors:

  • Jong Yoon Hyun;Hyun Kwang Kim

  • Affiliations:

  • Department of Mathematics, Pohang University of Science and Technology, Pohang, The Republic of Korea 790---784;Department of Mathematics, Pohang University of Science and Technology, Pohang, The Republic of Korea 790---784

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2008

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Abstract

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 $${\mathbb{P}}$$ -code if and only if $${C^\perp}$$ is an MDS $${\widetilde{\mathbb{P}}}$$ -code, where $${C^\perp}$$ is the dual code of C and $${\widetilde{\mathbb{P}}}$$ is the dual poset of $${\mathbb{P}.}$$