Geodesic
On list decoding of wavelet codes over finite fields of~characteristic two
Prikladnaâ diskretnaâ matematika, no. 2 (2019), pp. 94-106

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In this paper, we consider wavelet code defined over the field $\mathrm{GF}(2^m)$ with the code length $n =2^m-1$ and information words length $(n-1)/{2} $ and prove that a wavelet code allows list decoding in polynomial time if there are $d + 1$ consecutive zeros among the coefficients of the spectral representation of its generating polynomial and $0$. The steps of the algorithm that performs list decoding with correction up to $e$ errors are implemented as a program. Examples of its use for list decoding of noisy code words are given. It is also noted that the Varshamov–Hilbert inequality for sufficiently large $n$ does not allow to judge about the existence of wavelet codes with a maximum code distance $(n-1)/{2}$.
Mots-clés : wavelet codes
Keywords: polyphase coding, list decoding. 
@article{PDM_2019_2_a6,
     author = {D. V. Litichevskiy},
     title = {On list decoding of wavelet codes over finite fields of~characteristic two},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {94--106},
     publisher = {mathdoc},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2019_2_a6/}
}
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D. V. Litichevskiy. On list decoding of wavelet codes over finite fields of~characteristic two. Prikladnaâ diskretnaâ matematika, no. 2 (2019), pp. 94-106. http://geodesic.mathdoc.fr/item/PDM_2019_2_a6/