Prefer a chat interface with context about you and your work?
CYCLIC CODES OF LENGTH 2<sup>n</sup>OVER ℤ<sub>4</sub>
The purpose of this paper is to find a description of the cyclic codes of length <TEX>$2^n$</TEX> over <TEX>$\mathbb{Z}_4$</TEX>. We show that any ideal of <TEX>$\mathbb{Z}_4$</TEX>[X]/(<TEX>$X^{2n}$</TEX> - 1) is generated by at most two polynomials of the standard forms. We also find an explicit description of their duals in terms …