Some Open Problems on Quasi-Twisted and Related Code Constructions and Good Quaternary Codes

Oneofthemostimportant andchallenging prob- lemsincoding theory istoconstruct codes withthebestpossible parameters. Quasi-cyclic (QC)andthelarger class ofquasi- twisted (QT)codes havebeenproven tocontain manygoodcodes (with best-known parameters). Inthispaper, we review some openproblems concerning these codes, introduce generalizations ofQTcodes, andsuggest someconstructions involving QTcodes. We alsopresent somenewandgoodquaternary codes. Keywords:Quaternary codes,quasi-twisted codes,new bounds.