Minimal weight expansions in Pisot bases

For applications to cryptography, it is important to represent numbers with a small number of non-zero digits (Hamming weight) or with small absolute sum of digits. The problem of finding representations with minimal weight has been solved for integer bases, e.g. by the non-adjacent form in base 2. In this paper, we consider numeration systems with respect to real bases which are Pisot numbers and prove that the expansions with minimal absolute sum of digits are recognizable by finite automata. When is the Golden Ratio, the Tribonacci number or the smallest Pisot number, we determine expansions with minimal number of digits

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Christiane Frougny, Wolfgang Steiner
• Keywords: Absolute Sum, CORR 2008, Education, Finite Automata, Minimal Weight