Title: A Generalization of Quasi-twisted Codes: Multi-twisted codes,
Abstract: Cyclic codes and their various generalizations, such as quasi-twisted (QT)
codes, have a special place in algebraic coding theory. Among other things,
many of the best-known or optimal codes have been obtained from these classes.
In this work we introduce a new generalization of QT codes that we call
multi-twisted (MT) codes and study some of their basic properties. Presenting
several methods of constructing codes in this class and obtaining bounds on the
minimum distances, we show that there exist codes with good parameters in this
class that cannot be obtained as QT or constacyclic codes. This suggests that
considering this larger class in computer searches is promising for
constructing codes with better parameters than currently best-known linear
codes. Working with this new class of codes motivated us to consider a problem
about binomials over finite fields and to discover a result that is interesting
in its own right.