On ZpZpk-additive codes and their duality

Minjia Shi, Rongsheng Wu, Denis S. Krotov

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

In this paper, two different Gray-like maps from Z p α × Z pk β , where p is prime, to Z p n , n=α +β p k-1 , denoted by φ and Φ, respectively, are presented. We have determined the connection between the weight enumerators among the image codes under these two mappings. We show that if C is a Z p Z p k -additive code, and C⊥ is its dual, then the weight enumerators of the image p -ary codes φ (C) and Φ (C⊥) are formally dual. This is a partial generalization of [D. S. Krotov, On Z 2 k -dual binary codes, IEEE Transactions Information Theory 53 (2007), 1532-1537], and the result is generalized to odd characteristic p and mixed alphabet. In addition, a construction of 1-perfect additive codes in the mixed Z p Z p 2 ⋯ Z p k alphabet is given.

Original languageEnglish
Article number8554305
Pages (from-to)3841-3847
Number of pages7
JournalIEEE Transactions on Information Theory
Volume65
Issue number6
DOIs
Publication statusPublished - 1 Jun 2019

Keywords

  • Additives
  • Advanced Video Coding (AVC)
  • Binary codes
  • compression artifacts
  • convolutional neural networks (CNN)
  • Generators
  • High Efficiency Video Coding (HEVC)
  • Linear codes
  • Measurement
  • Propulsion
  • video compression
  • Zinc
  • linear codes
  • Gray map
  • MacWilliams identity
  • two-weight codes
  • 1-perfect codes
  • Dual codes

OECD FOS+WOS

  • 1.02.ET COMPUTER SCIENCE, INFORMATION SYSTEMS
  • 2.02.IQ ENGINEERING, ELECTRICAL & ELECTRONIC

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