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A class of doubly even self dual binary codes. (English) Zbl 0581.94011
We give a construction of an infinite class of doubly even self dual binary codes including a code of length 112. (The study of such a code is closely related to the existence problem of a projective plane of order ten.)

MSC:
94B05 Linear codes, general
51E15 Finite affine and projective planes (geometric aspects)
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[1] Assmus, E.F., On the possibility of a projective plane of order 10, (), Contract No F19628-69-C-0068
[2] Assmus, E.F., Self-orthogonal Steiner systems and projective planes, Math. Z., 138, 89-96, (1974) · Zbl 0273.50016
[3] Camion, P., Etude de codes binaries abeliens modulaires auto-duaux de petites longueurs, Rev. CETHEDEC, 79, 2, 3-24, (1979) · Zbl 0424.94009
[4] Lempel, A., Matrix factorization over GF(2) and trace orthogonal basis of GF(2), SIAM J. comput, 4, 175-186, (1975) · Zbl 0331.94006
[5] MacWilliams, F.J.; Sloane, N.J.A., The theory of error-correcting codes, (1977), North-Holland Amsterdam · Zbl 0369.94008
[6] MacWilliams, F.J.; Sloane, N.J.A.; Thompson, J.G., On the existence of a projective plane of order 10, J. combin. theory ser. A, 14, 66-78, (1973) · Zbl 0251.05020
[7] Pasquier, G., The binary golay code obtained from an extended cyclic code over F8, European J. combin., 1, 369-370, (1980) · Zbl 0439.94015
[8] Wolfmann, J., A new construction of the binary golay code (24, 12, 8) using a group algebra over a finite field, Discrete math., 31, 337-338, (1980) · Zbl 0444.94023
[9] Wolfmann, J., A permutation decoding of the (24, 12, 8) golay code, IEEE trans. inform. theory, 29, 748-750, (1983) · Zbl 0512.94010
[10] J. Wolfmann and G. Pasquier, A class of binary self dual codes, Rapport interne GECT, Université de Toulon.
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