V. A. Kopyttsev, V. G. Mikhailov, “Estimates for distribution of the minimal distance of a random linear code”, Diskr. Mat., 2015, Volume 27, Issue 2,Pages <nobr>45

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Estimates for distribution of the minimal distance of a random linear code

V. A. Kopyttsev^a, V. G. Mikhailov^b

^a Academy of Criptography of Russia
^b Steklov Mathematical Institute of RAS

Abstract: The distribution function of the minimum distance (the minimum weight of nonzero codewords) of a random linear code over a finite field is studied. Expicit bounds in the form of inequalities and asymptotic estimates for this distribution function are obtained.

Keywords: minimum distance of a linear code, explicit estimates of distribution functions, asymptotic estimates of distribution functions.

UDC: 519.21

Received: 11.03.2015

DOI: 10.4213/dm1324