Abstract
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.
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Acknowledgements
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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Crnković, D., Rukavina, S. & Šimac, M. LDPC Codes from \(\mu \)-Geodetic Graphs Obtained from Block Designs. Graphs and Combinatorics 35, 451–469 (2019). https://doi.org/10.1007/s00373-019-02007-4
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DOI: https://doi.org/10.1007/s00373-019-02007-4