On extremely transitive extended perfect codes

G. K. Guskov^a, F. I. Solov'eva<sup>ab

a</sup> Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
^b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

Abstract: It is constructed an infinite set of extended perfect codes of length $n=2^k$, $k\ge4$ that are extremely transitive, which means that all perfect codes obtained from these transitive extended codes by puncturing any coordinate are nontransitive. The classification of such codes of length 16 is done. Ill. 2, tab. 2, bibliogr. 14.

Keywords: extended perfect binary code, transitive code, Steiner triple system, Pasch configuration.

UDC: 519.8

Received: 27.08.2012
Revised: 28.05.2013

 English version: Journal of Applied and Industrial Mathematics, 2014, 8:1, 53–62

Bibliographic databases:

• 
•