2020/04/02 by Logan Gray Childers, Childers, L., K. Gopalakrishnan +1
Computer Science · #11B39 #94A45 (Primary) 68P30 (Secondary) #Algorithms and Data Compression #Coding theory and cryptography #Combinatorics (math.CO) #E.4 #FOS: Computer and information sciences #FOS: Mathematics #G.2.1 #H.1.1 #Information Theory (cs.IT) #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2004.00821
openalex publication_date 2020/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gopala-Hemachandra codes are a variation of the Fibonacci universal code and have applications in cryptography and data compression. We show that GHa(n) codes always exist for a=-2,-3 and -4 for any integer n ≥ 1 and hence are universal codes. We develop two new algorithms to determine whether a GH code exists for a given set of parameters a and n. In 2010, Basu and Prasad showed experimentally that in the range 1 ≤ n ≤ 100 and 1 ≤ k ≤ 16, there are at most k consecutive integers for which GH-(4+k)(n) does not exist. We turn their numerical result into a mathematical theorem and show that it is valid well beyond the limited range considered by them.