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New Classes of p-Ary Few Weight Codes

  • Minjia ShiEmail author
  • Rongsheng Wu
  • Liqin Qian
  • Lin Sok
  • Patrick Solé
Article

Abstract

In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring \(R=\mathbb {F}_p+u\mathbb {F}_p+\cdots +u^{k-1}\mathbb {F}_{p},\) with \(u^k=0,\) are constructed that generalize the construction of Shi et al. (IEEE Commun. Lett. 20(12):2346–2349, 2016), which is the special case of \(p=k=2.\) These codes are defined as trace codes. In some cases of their defining sets, they are abelian. Their homogeneous weight distributions are computed by using exponential sums. In particular, in the two-weight case, we give some conditions of optimality of their Gray images by using the Griesmer bound. Their dual homogeneous distance is also given. The codewords of these codes are shown to be minimal for inclusion of supports, a fact favorable to an application to secret sharing schemes.

Keywords

Two-weight codes Three-weight codes Homogeneous distance Gray map 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  • Minjia Shi
    • 1
    • 2
    • 3
    Email author
  • Rongsheng Wu
    • 2
  • Liqin Qian
    • 2
  • Lin Sok
    • 2
    • 4
  • Patrick Solé
    • 5
  1. 1.Key Laboratory of Intelligent Computing & Signal ProcessingMinistry of Education, Anhui UniversityHefeiP. R. China
  2. 2.School of Mathematical SciencesAnhui UniversityHefeiP. R. China
  3. 3.National Mobile Communications Research LaboratorySoutheast UniversityNanjingP. R. China
  4. 4.Department of MathematicsRoyal University of Phnom PenhPhnom PenhCambodia
  5. 5.CNRS/LAGAUniversity of Paris 8Saint-DenisFrance

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