Propelinear 1-perfect codes from quadratic functions

Denis Krotov; Vladimir Potapov

doi:10.1109/TIT.2014.2303158

Propelinear 1-perfect codes from quadratic functions

Information Theory 2014-03-17 v3 Discrete Mathematics Combinatorics math.IT

Authors: Denis Krotov , Vladimir Potapov

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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 $\exp(cN^2)$ 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.

Keywords

coding theory

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@article{arxiv.1301.0014,
  title  = {Propelinear 1-perfect codes from quadratic functions},
  author = {Denis Krotov and Vladimir Potapov},
  journal= {arXiv preprint arXiv:1301.0014},
  year   = {2014}
}

Comments

4 IEEE pages. v2: minor revision, + upper bound (Sect. III.B), +remarks (Sect. V.A); v3: minor revision, + length 15 (Sect. V.B)

Propelinear 1-perfect codes from quadratic functions

Abstract

Keywords

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