A meet-in-the-middle algorithm for finding extremal restricted additive 2-bases
Jukka Kohonen
TL;DR
This paper introduces a meet-in-the-middle algorithm to identify extremal restricted additive 2-bases with maximum range for given lengths, providing a comprehensive list up to length 41.
Contribution
The paper presents a novel meet-in-the-middle algorithm specifically designed to find extremal restricted additive 2-bases, advancing computational methods in additive number theory.
Findings
Algorithm successfully finds extremal restricted 2-bases up to length 41.
Lists of extremal restricted 2-bases for lengths up to 41 are provided.
The method improves computational efficiency in identifying extremal bases.
Abstract
An additive 2-basis with range n is restricted if its largest element is n/2. Among the restricted 2-bases of given length k, the ones that have the greatest range are extremal restricted. We describe an algorithm that finds the extremal restricted 2-bases of a given length, and we list them for lengths up to k = 41.
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Taxonomy
TopicsCoding theory and cryptography · Cryptography and Residue Arithmetic · Polynomial and algebraic computation