An Updated Database of $\mathbb{Z}_4$ Codes
Nuh Aydin, Yiang Lu, Vishad R. Onta

TL;DR
This paper introduces an extensively updated online database of $\\mathbb{Z}_4$ codes, adding 8701 new codes found through exhaustive searches and algorithm modifications, significantly expanding resources for coding theory research.
Contribution
The paper presents a major update to the $\\mathbb{Z}_4$ codes database, including new codes discovered via enhanced algorithms and exhaustive searches, especially non-free codes.
Findings
Added 8701 new $\\mathbb{Z}_4$ codes to the database.
Major updates include non-free codes, increasing diversity.
Modified ASR algorithm for $\\mathbb{Z}_4$ to find new codes.
Abstract
Research on codes over finite rings has intensified since the discovery in 1994 of the fact that some best binary non-linear codes can be obtained as images of -linear codes. Codes over many different finite rings has been a subject of much research in coding theory after this discovery. Many of these rings are extensions of . As a result, an online database of was created in 2008. The URL of the original database on codes has recently changed. The purpose of this paper is to introduce the new, updated database of codes. We have made major updates to the database by adding 8701 new linear codes over . These codes have been found through exhaustive computer searches on cyclic codes and by an implementation of the ASR search algorithm that has been remarkably fruitful to obtain new linear codes from the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · Quantum-Dot Cellular Automata · Educational Curriculum and Learning Methods
