Abstract
A series of mixed perfect codes with minimal distances \(d=3\) has been constructed in term of the partitions of vector space over finite field \(\mathbb {F}_{p}\) by B.Lindström. In this paper the minimal distance of the dual codes of a certain class of such perfect codes has been determined. As an application of this result we constructed a series of good orthogonal arrays with mixed levels and good inhomogeneous asymmetric quantum codes.
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References
Feng, K., Xu, L., Hickernell, F.: Linear error-block codes. Finite Fields Their Appl. 12, 638–652 (2006)
Hedayet, A.S., Sloane, N.J.A., Stufken, J.: Orthogonal Arrays: Theory and Applications. Springer Series in Statistics. Springer, New York (1999). https://doi.org/10.1007/978-1-4612-1478-6
Heden, O.: Partitions of finite Abelian groups. Eur. J. Comb. 7, 11–25 (1986)
Herzog, M., Schönheim, J.: Linear and nonlinear single error-correcting perfect mixed codes. Inf. Control. 18, 364–368 (1971)
Lindström, B.: Group partitions and mixed perfect codes. Can. Math. Bull. 18, 57–60 (1975)
El-Zanati, S.I., Seelinger, G.F., Sissokho, P.A., Spence, L.E., Vanden Eynden, C.: Partitions of finite vector spaces into subspaces. J. Comb. Des. 16, 329–341 (2008)
Wang, L., Feng, K., Ling, S., Xing, C.: Asymmetric quantum codes: characterization and constructions. IEEE Trans. Inf. Theory 56(6), 2938–2945 (2010)
Wang, W., Feng, R., Feng, K.: Inhomogenous quantum codes (I): additive case. Sci. China: Math. 53, 2501–2510 (2010)
Wang, W., Feng, K.: Inhomogenous quantum codes (III): asymmetric case (2010, preprint)
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Mao, T. (2018). Determination of Dual Distances for a Kind of Perfect Mixed Codes. In: Tang, S., Du, DZ., Woodruff, D., Butenko, S. (eds) Algorithmic Aspects in Information and Management. AAIM 2018. Lecture Notes in Computer Science(), vol 11343. Springer, Cham. https://doi.org/10.1007/978-3-030-04618-7_8
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DOI: https://doi.org/10.1007/978-3-030-04618-7_8
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