NDLI: On full-rank perfect codes over finite fields

Content Provider	Springer Nature Link
Author	Romav, A. M.
Copyright Year	2016
Abstract	We propose a construction of full-rank q-ary 1-perfect codes. This is a generalization of the construction of full-rank binary 1-perfect codes by Etzion and Vardy (1994). The properties of the i-components of q-ary Hamming codes are investigated, and the construction of full-rank q-ary 1-perfect codes is based on these properties. The switching construction of 1-perfect codes is generalized to the q-ary case. We propose a generalization of the notion of an i-component of a 1-perfect code and introduce the concept of an (i, σ)-component of a q-ary 1-perfect code. We also present a generalization of the Lindström–Schönheim construction of q-ary 1-perfect codes and provide a lower bound for the number of pairwise distinct q-ary 1-perfect codes of length n.
Starting Page	444
Ending Page	452
Page Count	9
File Format	PDF
ISSN	19904789
Journal	Journal of Applied and Industrial Mathematics
Volume Number	10
Issue Number	3
e-ISSN	19904797
Language	English
Publisher	Pleiades Publishing
Publisher Date	2016-08-24
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hamming code nonlinear perfect code full-rank code i-component Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Industrial and Manufacturing Engineering

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On full-rank perfect codes over finite fields