Table 1. Non-existence of extremal(or near-extremal) binaryself-dual codes with minimal(or near-minimal) shadow of lengthn = 24m+ p
References
- C. Bachoc and P. Gaborit, Designs and self-dual codes with long shadows, J. Combin. Theory ser. A 105 (2004), 15-34. https://doi.org/10.1016/j.jcta.2003.09.003
- E.R. Berlekamp, F.J. MacWilliams and N.J.A. Sloane, Gleason's theorem on self-dual codes, IEEE Trans. Inform. Theory 18 (1972), 409-414. https://doi.org/10.1109/TIT.1972.1054817
- S. Bouyuklieva, M. Harada and A. Munemasa, Nonexistence of certain singly even self-dual codes with minimal shadow, The Electronic Journal of Combinatorics 25 (2018), 1-13.
- S. Bouyuklieva and W. Willems, Singly even self-dual codes with minimal shadow, IEEE Trans. Inform. Theory 58 (2012), 3856-3860. https://doi.org/10.1109/TIT.2012.2183114
- J.H. Conway and N.J.A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory 36 (1990), 1319-1333. https://doi.org/10.1109/18.59931
- J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, New York: Springer-Verlag, 1988.
- S. Han, Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF(2) and GF(4), MDPI Information 9, 172 (2018), 1-12. https://doi.org/10.3390/info9010001
- W.C. Human, On the classification and enumeration of self-dual codes, Finite Fields Appl. 11 (2005), 451-490. https://doi.org/10.1016/j.ffa.2005.05.012
- F.J. MacWilliams and N.J.A. Sloane, The theory of error correcting codes, North-Holland; 9th ed., 1998.
- E.M. Rains, Shadow bounds for self-dual codes, IEEE Trans. Inform. Theory 44 (1998), 134-139. https://doi.org/10.1109/18.651000
- N. Elkies, Lattices and codes with long shadows, Math. Res. Lett. 2 (1995), 643651.