A low-rate improvement on the Elias bound (Corresp.)

Abstract

An upper bound on the minimum distance of binary blocks codes, which is superior to Elias' bound for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R &lt; 0.0509^+</tex> , is obtained. The new hound has the same derivative <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(-\infty)</tex> at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R = 0</tex> as Gilbert's lower bound. (Elias' bound has derivative <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-\ln 2</tex> at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R = 0)</tex> .