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 $\exp(cN^2)$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2012
- DOI:
- 10.48550/arXiv.1301.0014
- arXiv:
- arXiv:1301.0014
- Bibcode:
- 2013arXiv1301.0014K
- Keywords:
-
- Computer Science - Information Theory;
- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics;
- 94B25
- E-Print:
- 4 IEEE pages. v2: minor revision, + upper bound (Sect. III.B), +remarks (Sect. V.A)