Algebraic techniques for nonlinear codes


We introduce some techniques for nonlinear systematic error-correcting codes over the two-element alphabet. As an application, we construct new perfect 1-error-correcting (15,11)-codes.

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  1. [1]

    F. C. Bussemaker andJ. J. Seidel, Symmetric Hadamard matrices of order 36,Technological University Edindhoven Report 70 WSK-02 (1970).

  2. [2]

    G. Grumbach, 1-Fehler-korrigierende, perfekte Codes überF q ,Diplomarbeit TH Darmstadt (1980)(unpublished).

  3. [3]

    F. Hergert, Beiträge zur Theorie nichtlinearer Fehler-korrigierender Codes,Diplomarbeit TH Darmstadt (1980)(unpublished).

  4. [4]

    M. Limbos, Projective embeddings of small “Steiner Triple Systems”,Annals of Discrete Mathematics 7 (1980), 151–173.

    MATH  MathSciNet  Article  Google Scholar 

  5. [5]

    F. J. MacWilliams andN. J. A. Sloane,The theory of error-correcting codes, North-Holland Publ. Comp. (1978).

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Bauer, H., Ganter, B. & Hergert, F. Algebraic techniques for nonlinear codes. Combinatorica 3, 21–33 (1983).

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AMS subject classification 1980

  • 94 B 60