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Propelinear 1-Perfect Codes From Quadratic Functions

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2 Author(s)
Krotov, D.S. ; Sobolev Inst. of Math., Novosibirsk, Russia ; Potapov, V.N.

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(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(NlnN)2vphantom)).

Published in:

Information Theory, IEEE Transactions on  (Volume:60 ,  Issue: 4 )

Date of Publication:

April 2014

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