Propelinear 1-perfect codes from quadratic functions

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 $\exp (c{N}^2)$ 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.

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

References in corpus (1)

• Z4-Linear Perfect Codes

Cited by in corpus (3)

• Constructions of transitive latin hypercubes
• Transitive nonpropelinear perfect codes
• A concatenation construction for propelinear perfect codes from regular subgroups of GA(r,2)