Bivariate Variations of Fibonacci and Narayana Sequences and Universal Codes

Abstract

In this study, we worked on the third-order bivariate variant of the Fibonacci universal code and the second-order bivariate variant of the Narayana universal code, depending on two negative integer variables u and v. We then showed in tables these codes for 1≤k≤100, u=-1,-2,…,-20, and v=-2,-3,…,-21 (u and v are consecutive, v$<$u). Moreover, we obtained some significant results from these tables. Furthermore, we compared the use of these codes in cryptography. Finally, we obtained the third-order bivariate variant of Fibonacci codes is more valuable than the second-order bivariate variant of Narayana codes.

Keywords

• Fibonacci sequence
• Narayana sequence
• cryptography
• variant Fibonacci code
• variant Narayana Code

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