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Hamming graphs and special LCD codes

  • W. Fish
  • J. D. KeyEmail author
  • E. Mwambene
  • B. G. Rodrigues
Original Research
  • 23 Downloads

Abstract

Codes from adjacency matrices from the Hamming graphs \(H^k(n,m)\) are examined for the property of being special LCD codes. The special property involves being able to propose a feasible decoding algorithm for the binary codes, and also to deduce the dimension of the code from the eigenvalues of an adjacency matrix, which are known for these graphs. Some positive results are obtained, in particular for the binary and ternary codes.

Keywords

LCD codes Hamming graphs Decoding 

Mathematics Subject Classification

05C50 94B05 

Notes

Acknowledgements

B. G. Rodrigues acknowledges research support of the National Research Foundation of South Africa (Grant Numbers 95725 and 106071).

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Copyright information

© Korean Society for Informatics and Computational Applied Mathematics 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Applied MathematicsUniversity of the Western CapeBellvilleSouth Africa
  2. 2.School of Mathematics, Statistics and Computer ScienceUniversity of KwaZulu-NatalDurbanSouth Africa

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