Partial permutation decoding for binary linear and Z<inf>4</inf> -linear Hadamard codes

Roland D. Barrolleta, Mercè Villanueva

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11 Citations (Scopus)


© 2017, Springer Science+Business Media New York. In this paper, s-PD -sets of minimum size s+ 1 for partial permutation decoding for the binary linear Hadamard code Hm of length 2 m, for all m≥ 4 and 2≤s≤⌊2m1+m⌋-1, are constructed. Moreover, recursive constructions to obtain s-PD -sets of size l≥ s+ 1 for Hm+1 of length 2 m+1, from an s-PD -set of the same size for Hm, are also described. These results are generalized to find s-PD -sets for the Z4-linear Hadamard codes Hγ,δ of length 2 m, m= γ+ 2 δ- 1 , which are binary Hadamard codes (not necessarily linear) obtained as the Gray map image of quaternary linear codes of type 2 γ4 δ. Specifically, s-PD-sets of minimum size s+ 1 for Hγ,δ, for all δ≥ 3 and 2≤s≤⌊22δ-2δ⌋-1, are constructed and recursive constructions are described.
Original languageEnglish
Pages (from-to)569-586
JournalDesigns, Codes, and Cryptography
Issue number3
Publication statusPublished - 1 Mar 2018


  • Automorphism group
  • Hadamard code
  • PD -set
  • Permutation decoding
  • Z -linear code 4


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