© 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.
|Journal||Designs, Codes, and Cryptography|
|Publication status||Published - 1 Mar 2018|
- Automorphism group
- Hadamard code
- PD -set
- Permutation decoding
- Z -linear code 4