PD-sets for Z4-linear codes: Hadamard and Kerdock codes
نویسندگان
چکیده
Permutation decoding is a technique that strongly depends on the existence of a special subset, called PD-set, of the permutation automorphism group of a code. In this paper, a general criterion to obtain s-PD-sets of size s + 1, which enable correction up to s errors, for Z4-linear codes is provided. Furthermore, some explicit constructions of s-PD-sets of size s+1 for important families of (nonlinear) Z4-linear codes such as Hadamard and Kerdock codes are given.
منابع مشابه
On the permutation decoding for binary linear and Z4-linear Hadamard codes
Permutation decoding is a technique, introduced in [3] by MacWilliams, that strongly depends on the existence of special subsets, called PD-sets, of the permutation automorphism group PAut(C) of a linear code C. In [2], it is shown how to find s-PD-sets of minimum size s + 1 for partial permutation decoding for the binary simplex code Sm of length 2 − 1, for all m ≥ 4 and 1 < s ≤ ⌊ 2−m−1 m ⌋ . ...
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