Propelinear 1-perfect codes from quadratic functions
Abstract
Perfect codes obtained by the Vasil'ev--Sch\"onheim construction from a linear base code and quadratic switching functions are transitive and, moreover, propelinear. This gives at least (cN2) propelinear 1-perfect codes of length N over an arbitrary finite field, while an upper bound on the number of transitive codes is (C(N N)2). Keywords: perfect code, propelinear code, transitive code, automorphism group, Boolean function.
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