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Designs, Codes and Cryptography

, Volume 45, Issue 1, pp 51–64 | Cite as

G-projectable and Λ-projectable binary linear block codes

  • Morteza Esmaeili
  • Morteza Hivadi
Article
  • 78 Downloads

Abstract

The binary [24,12,8] Golay code has projection O onto the quaternary [6,3,4] hexacode [9] and the [32,16,8] Reed-Muller code has projection E onto the quaternary self-dual [8,4,4] code [6]. Projection E was extended to projection G in [8]. In this paper we introduce a projection, to be called projection Λ, that covers projections O, E and G. We characterise G-projectable self-dual codes and Λ-projectable codes. Explicit methods for constructing codes having G and Λ projections are given and several so constructed codes that have best known optimal parameters are introduced.

Keywords

Linear block code Projection on F_4 G-Projection Λ-Projection 

AMS Classification

94B35 

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References

  1. Amrani O and Be’ery Y (2001). Reed-Muller codes: Projections on GF(4) and multilevel construction. IEEE Trans Inform Theory 47: 2560–2565 MATHCrossRefGoogle Scholar
  2. Brouwer AE Linear code bound. http://www.win.tue.nl/aeb/voorlincod.html.Google Scholar
  3. Esmaeili M, Gulliver TA and Khandani AK (2003). On the Pless construction and ML Decoding of the (48,24,12) quadratic residue code. IEEE Trans Inform Theory 49: 1527–1535 MATHCrossRefGoogle Scholar
  4. Esmaeili M, Gulliver TA On the quaternary projection of binary linear block codes. ARS Combinatoria, Vol.~85, October~2007Google Scholar
  5. Gaborit P, Huffman WC, Kim J-L, Pless V (2001) On additive GF(4) codes. In: proceedings of the DIMACS workshop on codes and association schemes, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 56, AMS Providence, RI, pp 135–149Google Scholar
  6. Gaborit P, Kim J-L and Pless V (2003). Decoding binary R(2,5) by hand. Discrete Math 264: 55–73 MATHCrossRefGoogle Scholar
  7. Kim J-L, Pless V (2002) Decoding some doubly-even self-dual [32,16,8] codes by hand. In: proceedings of a conference honouring Professor Dijen Ray-Chaudhuri on the occasion of his 65th birthday, Ohio State Univ. Math. Res. Inst. Publ. 10, Ohio State University, Columbus, OH, pp 165–178Google Scholar
  8. Kim J-L, Mellinger KE and Pless V (2003). Projections of binary linear codes onto larger fields. SIAM J Discrete Math 16(4): 591–603 MATHCrossRefGoogle Scholar
  9. Pless V (1986). Decoding the Golay codes. IEEE Trans Inform Theory 32: 561–566 MATHCrossRefGoogle Scholar
  10. Vardy A and Be’ery Y (1991). More efficient soft decoding of the Golay codes. IEEE Trans Inform Theory 37: 667–672 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran

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