%0 Journal Article %T The Gopala-Hemachandra universal code determined by straight lines %A Pal, Joydeb %A Das, Monojit %J Journal of Mathematics and Computer Science %D 2019 %V 19 %N 3 %@ ISSN 2008-949X %F Pal2019 %X Variation on the Fibonacci universal code, known as Gopala-Hemachandra (or GH) code, is mainly used in data compression and cryptography as it is a self-synchronizing code. In 2010, Basu and Prasad showed that Gopala-Hemachandra code \(GH_a(n)\) exists for \(-20 \leq a \leq -2\) and \(1 \leq n \leq 100\) as well as there are \(m\) consecutive non-existing Gopala-Hemachandra codewords in \(GH_{-(4+m)}(n)\) column where \(1 \leq m \leq 16\). In this paper, we have introduced GH code straight line in two-dimensional space where each integral point \((a, n)\) on the GH code straight line represents a unique GH codeword. GH code straight lines confirm the existence of GH codewords for any integer \(n \geq 1\) and integer \(a \leq -2\). Moreover, for a given parameter \((a, n)\), we have introduced two methods to check whether GH codeword exists or not. %9 journal article %R 10.22436/jmcs.019.03.03 %U http://dx.doi.org/10.22436/jmcs.019.03.03 %P 158--170