Optimization of Generalized Unary Coding

TL;DR

This paper introduces an optimized generalized unary coding scheme that extends the count of representable numbers by allowing the block of 1s to be broken up, supported by a formal theorem.

Contribution

It presents an optimal version of generalized unary coding with a new counting formula, improving the previous scheme.

Findings

Extended number count to n(n-k-1)+1

Established a formal theorem for the new scheme

Demonstrated improved coding capacity

Abstract

This paper proposes an optimum version of the recently advanced scheme for generalized unary coding. In this method, the block of 1s that identifies the number is allowed to be broken up, which extends the count. The result is established by a theorem. The number count is now n(n-k-1)+1 rather than the previously described (n-k)(n-k)-1.