Representations of Genetic Tables, Bimagic Squares, Hamming Distances and Shannon Entropy

TL;DR

This paper explores the relationships between genetic tables, magic and bimagic squares, Hamming distances, and Shannon entropy, revealing new connections and symmetries in these mathematical and biological structures.

Contribution

It introduces novel links between genetic tables and magic squares, applies Gray code, and calculates Shannon entropy for various magic square orders.

Findings

Established relations between genetic tables and magic squares

Connected Hamming distances and binomial coefficients with genetic structures

Calculated Shannon entropy for 4x4, 8x8, and 16x16 magic squares

Abstract

In this paper we have established relations of the genetic tables with magic and bimagic squares. Connections with Hamming distances, binomial coefficients are established. The idea of Gray code is applied. Shannon entropy of magic squares of order 4x4, 8x8 and 16x16 are also calculated. Some comparison is also made. Symmetry among restriction enzymes having four letters is also studied.