Propelinear 1-perfect codes from quadratic functions

Denis Krotov; Vladimir Potapov

doi:10.1109/tit.2014.2303158

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arXiv · 1301.0014

Propelinear 1-perfect codes from quadratic functions

Denis Krotov·Vladimir Potapov

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Abstract

Perfect codes obtained by the Vasil'ev--Schönheim construction from a linear base code and quadratic switching functions are transitive and, moreover, propelinear. This gives at least $\exp(cN^2)$ 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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Denis Krotov, Vladimir Potapov. 2014-02-20. Propelinear 1-perfect codes from quadratic functions. https://doi.org/10.1109/tit.2014.2303158

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