Propelinear 1-Perfect Codes From Quadratic Functions

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...

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Bibliographic Details
Published in:IEEE transactions on information theory 2014-04, Vol.60 (4), p.2065-2068
Main Authors: Krotov, Denis S., Potapov, Vladimir N.
Format: Article
Language:English
Subjects:
automorphism group
Branch & bound algorithms
Educational institutions
Error correction codes
Information theory
Mathematical functions
Perfect code
propelinear code
Propulsion
Regression analysis
Space vehicles
transitive code
Upper bound
Vectors
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Summary: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(NlnN) 2\vphantom) ).
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2303158