Some Good Cyclic and Quasi-Twisted Z4-Linear Codes

For over a decade, there has been considerable research on codes over Z4 and other rings. In spite of this, no tables or databases exist for codes over Z4, as is the case with codes over finite fields. The purpose of this work is to contribute to the creation of such a database. We consider cyclic, negacyclic and quasi-twisted (QT) codes over Z4. Some of these codes have binary images with better parameters than the best-known binary linear codes. We call such codes “good codes”. Among these are two codes which improve the bounds on the best-known binary non-linear codes. Tables of best cyclic and QT codes over Z4 are presented.

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