zbMATH — the first resource for mathematics

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.)

94B05 Linear codes, general
51E15 Finite affine and projective planes (geometric aspects)
Full Text: DOI
[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.