Skip to main content
SpringerLink
Log in

Minimum distances of three families of low-density parity-check codes based on finite geometries

  • Research Article
  • Published:
Frontiers of Mathematics in China Aims and scope Submit manuscript

Abstract

Three families of low-density parity-check (LDPC) codes are constructed based on the totally isotropic subspaces of symplectic, unitary, and orthogonal spaces over finite fields, respectively. The minimum distances of the three families of LDPC codes in some special cases are settled.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aly S A. A class of quantum LDPC codes constructed from finite geometries. Global Telecomm Conf, 2008, 1–5

    Google Scholar 

  2. Gallager R G. Low density parity check codes. IRE Trans Inform Theory, 1962, 8: 21–28

    Article  MathSciNet  MATH  Google Scholar 

  3. Keha A B, Duman T M. Minimum distance computation of LDPC codes using a branch and cut algorithm. IEEE Trans Commun, 2010, 58: 1072–1079

    Article  Google Scholar 

  4. Kim J L, Mellinger K E, Storme L. Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles. Des Codes Cryptogr, 2007, 42: 73–92

    Article  MathSciNet  MATH  Google Scholar 

  5. Kim J L, Peled U N, Perepelitsa I, Pless V, Friedland S. Explicit construction of families of LDPC codes with no 4-cycles. IEEE Trans Inform Theory, 2004, 50: 2378–2388

    Article  MathSciNet  MATH  Google Scholar 

  6. Kou Y, Lin S, Fossorier M.P. Low-density parity-check codes based on finite geometries: a rediscovery and new results. IEEE Trans Inform Theory, 2001, 47: 2711–2736

    Article  MathSciNet  MATH  Google Scholar 

  7. Liu L, Huang J, Zhou W, Zhou S. Computing the minimum distance of nonbinary LDPC codes. IEEE Trans Commun, 2012, 60: 1753–1758

    Article  Google Scholar 

  8. Liva G, Song S, Lan L, Zhang Y, Ryan W, Lin S, Ryan W E. Design of LDPC codes: a survey and new results. J Commun Softw Syst, 2006, 2: 191–211

    Google Scholar 

  9. Sin P, Xiang Q. On the dimensions of certain LDPC codes based on q-regular bipartite graphs. IEEE Trans Inform Theory, 2006, 52: 3735–3737

    Article  MathSciNet  MATH  Google Scholar 

  10. Wan Z. Geometry of Classical Groups over Finite Fields. Beijing: Science Press, 2002

    Google Scholar 

  11. Yang K, Helleseth T. On the minimum distance of array codes as LDPC codes. IEEE Trans Inform Theory, 2003, 49: 3268–3271

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, China

    Yanan Feng & Changli Ma

  2. School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang, 050031, China

    Shuo Deng

  3. Department of Mathematics and Computer Science, Hengshui University, Hengshui, 053000, China

    Lu Wang

Authors
  1. Yanan Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuo Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Changli Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Changli Ma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Feng, Y., Deng, S., Wang, L. et al. Minimum distances of three families of low-density parity-check codes based on finite geometries. Front. Math. China 11, 279–289 (2016). https://doi.org/10.1007/s11464-016-0530-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11464-016-0530-2

Keywords

MSC

Search

Navigation