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Comparing decoding methods for quaternary linear codes. (English) Zbl 1419.94087

de Mier, Anna (ed.) et al., Discrete mathematics days. Extended abstracts of the 10th “Jornadas de matemática discreta y algorítmica” (JMDA), Barcelona, Spain, July 6–8, 2016. Amsterdam: Elsevier. Electron. Notes Discrete Math. 54, 283-288 (2016).
Summary: Permutation decoding is a technique which involves finding a subset \(S\), called PD-set, of the permutation automorphism group of a code \(C\). Constructions of small PD-sets for partial decoding for two families of \(\mathbb{Z}_4\)-linear codes (Hadamard and Kerdock) are given. Moreover, different decoding methods for \(\mathbb{Z}_4\)-linear codes are compared by showing their performance applied to these two families.
For the entire collection see [Zbl 1354.05002].

MSC:

94B35 Decoding
94B05 Linear codes (general theory)

Software:

Magma; Codes over Z4
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References:

[1] Babu, N. S.; Zimmermann, K. H., Decoding of linear codes over Galois rings, IEEE Trans. Inform. Theory., 47, 1599-1603, (2001) · Zbl 1017.94023
[2] Barrolleta, R.; Pernas, J.; Pujol, J.; Villanueva, M., Codes over \(\mathbb{Z}_4\). A magma package, (2015), Autonomous University of Barcelona
[3] Barrolleta, R.; Villanueva, M., Partial permutation decoding for binary linear and \(\mathbb{Z}_4\)-linear Hadamard codes, (2015) · Zbl 1338.94105
[4] Barrolleta, R.; Villanueva, M., PD-sets for \(\mathbb{Z}_4\)-linear codes: Hadamard and kerdock codes, (Proceedings of the IEEE International Symposium on Information Theory, (2016))
[5] Bernal, J. J.; Borges, J.; Fernández-Córboda, C.; Villanueva, M., Permutation decoding of \(\mathbb{Z}_2 \mathbb{Z}_4\)-linear codes, Des. Codes and Cryptogr., 76, 269-277, (2015)
[6] Cannon, J. J.; Bosma, W., Handbook of magma functions, 4350, (2006)
[7] Hammons, A. R.; Kumar, P. V.; Calderbank, A. R.; Sloane, N. J.A.; Solé, P., The \(\mathbb{Z}_4\)-linearity of kerdock, preparata, goethals and related codes, IEEE Trans. Inform. Theory, 40, 301-319, (1994) · Zbl 0811.94039
[8] Fish, W.; Key, J. D.; Mwambene, E., Partial permutation decoding for simplex codes, Adv. Math. Commun., 6, 505-516, (2012) · Zbl 1282.94089
[9] Krotov, D. S., \(\mathbb{Z}_4\)-linear Hadamard and extended perfect codes, Electron. Note Discr. Math., 6, 107-112, (2001)
[10] MacWilliams, F. I.; Sloane, N. J., The theory of error-correcting codes, (1977), North-Holland New York · Zbl 0369.94008
[11] Villanueva, M.; Zeng, F.; Pujol, J., Efficient representation of binary nonlinear codes: constructions and minimum distance computation, Des. Codes and Cryptogr., 76, 3-21, (2015) · Zbl 1346.94153
[12] Zimmerman, K.-H., Integral Hecke modules, integral generalized Reed-muller codes, and linear codes, (1996), Technische Universität Hamburg-Harburg, Tech. Rep. 3-96
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