Spreads , Translation Planes and Kerdock Sets
نویسنده
چکیده
In an orthogonal vector space of type l)/(4n, q), a spread is a family of q2n-l+ totally singular 2n-spaces which induces a partition of the singular points; these spreads are closely related to Kerdock sets. In a 2m-dimensional vector space over GF(q), a spread is a family of q + subspaces of dimension m which induces a partition of the points of the underlying projective space; these spreads correspond to affine translation planes. By combining geometric, group theoretic and matrix methods, new types of spreads are constructed and old examples are studied. New Kerdock sets and new translation planes are obtained having various interesting properties.
منابع مشابه
Kerdock codes and related planes
Kantor, W.M., Kerdock codes and related planes, Discrete Mathematics 106/107 (1992) 297-302. Among the many aspects of coding theory Jack van Lint has studied intensively are some generalizations of Preparata and Kerdock codes (see Baker et al. (1983), Cameron and Van Lint (1991) and Van Lint (1983)). There are still many open problems concerning these. This note is a brief discussion of proble...
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