Turkish Journal of Mathematics
Abstract
Let R_{k,m} be the ring F_{2^m}[u_1,u_2,...,u_k]/\gen u_i^2, u_iu_j-u_ju_i. In this paper, cyclic codes of arbitrary length n over the ring R_{2,m} are completely characterized in terms of unique generators and a way for determination of these generators is investigated. A F_{2^m}-basis for these codes is also derived from this representation. Moreover, it is proven that there exists a one-to-one correspondence between cyclic codes of length 2n, n odd, over the ring R_{k-1,m} and cyclic codes of length n over the ring R_{k,m}. By determining the complete structure of cyclic codes of length 2 over R_{2,m}, a mass formula for the number of these codes is given. Using this and the mentioned correspondence, the number of ideals of the rings R_{2,m} and R_{3,m} is determined. As a corollary, the number of cyclic codes of odd length n over the rings R_{2,m} and R_{3,m} is obtained.
DOI
10.3906/mat-1211-20
Keywords
Cyclic codes, codes over R_{2, m}
First Page
1061
Last Page
1074
Recommended Citation
SOBHANI, R, & MOLAKARIMI, M (2013). Some results on cyclic codes over the ring R_{2,m}. Turkish Journal of Mathematics 37 (6): 1061-1074. https://doi.org/10.3906/mat-1211-20
