Abstract
Quaternary codes have been studied recently in connection with the construction of sequences with low correlation, lattices and good non linear codes (Kerdock, Preparata). In this paper, we construct formally self-dual binary codes and unimodular lattices using quaternary codes. Two different processes are studied: constructions using Hensel lifting and (u¦u+v) construction. We give a number of examples of formally self-dual binary codes of length n≤64. We obtain a new construction of the Leech lattice, and two new constructions of the Gosset lattice.
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R. Hammons, P.V.Kumar, A.R. Calderbank, N.J.A Sloane, and P. Solé. Kerdock, Preparata, Goethals and Other Codes are linear over Z4. submitted to IEEE Transactions on information theory, 1992.
G. T. Kennedy and V. Pless. On Designs and Formally Self-Dual Codes, preprint, 1992.
V. Pless. A Classification of Self-Orthogonal Codes over GF(2). Discrete Math, pages 209–246, 1972.
J.H. Conway and N.J.A Sloane. Self-dual codes over the integers modulo 4. JCT A 62, 30–45, 1993.
F.J. MacWilliams and N.J.A. Sloane. The theory of Error-Correcting Codes. North-Holland, 1977.
M.Klemm. Selbstduale Codes über dem Ring der ganzen Zalen modulo 4. Arch. Math., 53:201–207, 1989.
J.H.Conway and N.J.A. Sloane. Sphere Packings, Lattices and Groups. Springer-Verlag, 1988.
JR D. Forney. Coset Codes — Part II: Binary lattices and related codes. IEEE, Transactions on information theory, 34:1152–1187, 1988.
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© 1994 Springer-Verlag Berlin Heidelberg
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Bonnecaze, A., Solé, P. (1994). Quaternary constructions of formally self-dual binary codes and unimodular lattices. In: Cohen, G., Litsyn, S., Lobstein, A., Zémor, G. (eds) Algebraic Coding. Algebraic Coding 1993. Lecture Notes in Computer Science, vol 781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57843-9_20
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DOI: https://doi.org/10.1007/3-540-57843-9_20
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Online ISBN: 978-3-540-48357-1
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