2022/08/14 by Nuh Aydın, Aydin, Nuh, Yiang Lu +3
Computer Science · Social Sciences · #94B60 #94B65 #Coding theory and cryptography #Educational Curriculum and Learning Methods #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2208.06832
openalex publication_date 2022/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℤ4-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 ℤ4. As a result, an online database of ℤ4 was created in 2008. The URL of the original database on ℤ4 codes has recently changed. The purpose of this paper is to introduce the new, updated database of ℤ4 codes. We have made major updates to the database by adding 8701 new linear codes over ℤ4. 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 class of quasi-cyclic (QC) and quasi-twisted (QT) codes over finite fields. We made modifications to the ASR algorithm to make it work over ℤ4. The initial database contained few codes that were not free. We have added a large number of non-free codes. In fact, of the 8701 codes we have added, 7631 of them are non-free.