FREE CYCLIC CODES OVER FINITE LOCAL RINGS
FREE CYCLIC CODES OVER FINITE LOCAL RINGS
In [2] it was shown that a 1-generator quasi-cyclic code C of length n = ml of index l over <TEX>$\mathbb{Z}_4$</TEX> is free if C is generated by a polynomial which divides <TEX>$X^m-1$</TEX>. In this paper, we prove that a necessary and sufficient condition for a cyclic code over <TEX>$\mathbb{Z}_pk$</TEX> …