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Title of Journal: Des Codes Cryptogr

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Abbravation: Designs, Codes and Cryptography

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Springer US

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DOI

10.1002/2015JD023147

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1573-7586

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Algebraic decoding of folded Gabidulin codes

Authors: Hannes Bartz Vladimir Sidorenko
Publish Date: 2016/03/23
Volume: 82, Issue: 1-2, Pages: 449-467
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Abstract

An efficient interpolationbased decoding algorithm for hfolded Gabidulin codes is presented that can correct rank errors beyond half the minimum rank distance for any code rate 0le Rle 1 The algorithm serves as a list decoder or as a probabilistic unique decoder and improves upon existing schemes especially for high code rates A probabilistic unique decoder with adjustable decoding radius is presented The decoder outputs a unique solution with high probability and requires at most mathcal Os2n2 operations in mathbb F qm where 1le sle h is a decoding parameter and nle m is the length of the unfolded code over mathbb F qm An upper bound on the average list size of folded Gabidulin codes and on the decoding failure probability of the decoder is given Applying the ideas to a list decoding algorithm by Mahdavifar and Vardy Listdecoding of subspace codes and rankmetric codes up to Singleton bound ISIT 2012 improves the performance when used as probabilistic unique decoder and gives an upper bound on the failure probabilityThe authors would like to thank Gerhard Kramer Joschi Brauchle and Johan S R Nielsen for fruitful discussions and helpful comments H Bartz was supported by the German Ministry of Education and Research in the framework of an Alexander von HumboldtProfessorship

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  1. Composition of recursions and nonlinear complexity of periodic binary sequences
  2. Practical-time attacks against reduced variants of MISTY1
  3. On the largest affine sub-families of a family of NFSR sequences
  4. The dimension of subcode-subfields of shortened generalized Reed–Solomon codes
  5. On explicit factors of cyclotomic polynomials over finite fields
  6. Two classes of optimal two-dimensional OOCs
  7. Sequences with small correlation
  8. Improved algorithms for finding low-weight polynomial multiples in $$\mathbb {F}_{2}^{}[x]$$ and some cryptographic applications
  9. A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
  10. Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
  11. A new table of permutation codes
  12. Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
  13. Nonexistence of CW (110, 100)
  14. Point compression for the trace zero subgroup over a small degree extension field
  15. The Diffie–Hellman problem and generalization of Verheul’s theorem
  16. Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
  17. Improved lower bounds on sizes of single-error correcting codes
  18. A combinatorial problem related to sparse systems of equations
  19. Some results concerning cryptographically significant mappings over GF(2 n )
  20. A note on the reducibility of binary affine polynomials
  21. Primitive normal bases for quartic and cubic extensions: a geometric approach
  22. Computing isogenies between supersingular elliptic curves over $${\mathbb {F}}_p$$
  23. Some cyclic codes of length 2 p n
  24. On the correlation distribution of Delsarte–Goethals sequences
  25. Inner balance of symmetric designs
  26. On the construction of Griesmer codes of dimension 5
  27. Applications of representation theory to wireless communications
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