A q-polynomial approach to cyclic codes

Cyclic codes have been an interesting topic of both mathematics and engineering for decades. They are prominently used in consumer electronics, data transmission technologies, broadcast systems, and computer applications. Three classical approaches to the study and construction of cyclic codes are those based on the generator matrix, the generator polynomial and the idempotent. The objective of this paper is to develop another approach – the q-polynomial approach. Fundamental theory of this approach will be developed, and will be employed to construct a new family of cyclic codes in this paper.