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Propelinear 1-perfect codes from quadratic functions (1301.0014v3)
Published 31 Dec 2012 in cs.IT, cs.DM, math.CO, and math.IT
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 $\exp(cN2)$ propelinear $1$-perfect codes of length $N$ over an arbitrary finite field, while an upper bound on the number of transitive codes is $\exp(C(N\ln N)2)$. Keywords: perfect code, propelinear code, transitive code, automorphism group, Boolean function.
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