Graphs and Combinatorics

, Volume 35, Issue 2, pp 451–469 | Cite as

LDPC Codes from \(\mu \)-Geodetic Graphs Obtained from Block Designs

  • Dean Crnković
  • Sanja Rukavina
  • Marina ŠimacEmail author
Original Paper


In this paper we study low-density parity-check (LDPC) codes spanned by rows of the adjacency matrices of \(\mu \)-geodetic graphs obtained from 2-\((v,k,\lambda )\) designs. This construction can be applied to any 2-\((v,k,\lambda )\) design, but in this paper we focus on the LDPC codes from \(\mu \)-geodetic graphs obtained from 2-\((v,3,\lambda )\) designs since their Tanner graphs are free of 4-cycles. We analyse some properties of the constructed LDPC codes and discuss code length, dimension and minimum distance. Further, we discuss absorbing sets of these LDPC codes and give an expression for the expectation of a syndrome weight of the constructed LDPC codes. Information on the constructed LDPC codes, such as their parameters, is presented as well.


LDPC code \(\mu \)-Geodetic graph Block design 

Mathematics Subject Classification

94B05 05C99 05B05 



This work has been fully supported by Croatian Science Foundation under the project 6732. The authors would like to thank the anonymous referees for the helpful comments and suggestions.


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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of RijekaRijekaCroatia

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