Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(2): 391-397

Online first article July 4, 2018      Printed March 1, 2019

https://doi.org/10.4134/BKMS.b180284

Copyright © The Korean Mathematical Society.

A simple proof of the improved Johnson bound for binary codes

Le Thi Ngoc Giau, Phan Thanh Toan

Ton Duc Thang University; Ton Duc Thang University

Abstract

In this paper, we give a simple proof of the improved Johnson bound for $A(n,d)$, the maximum number of codewords in a binary code of length $n$ and minimum distance $d$, given by Mounits, Etzion and Litsyn.

Keywords: binary code, Johnson bound, upper bound

MSC numbers: 94B65

Supported by: This research is funded by Foundation for Science and Technology Development of Ton Duc Thang University (FOSTECT), website: http://fostect.tdtu.edu.vn, under Grant FOSTECT.2017.BR.02.