@article {IOPORT.05591600, author = {Abualrub, Taher and Siap, Irfan}, title = {Constacyclic codes over $F_2 + uF_2$.}, year = {2009}, journal = {Journal of the Franklin Institute}, volume = {346}, number = {5}, issn = {0016-0032}, pages = {520-529}, publisher = {Elsevier Science Ltd. (Pergamon), Oxford}, doi = {10.1016/j.jfranklin.2009.02.001}, abstract = {Summary: We study the structure of $(1+u)$-constacyclic codes of an arbitrary length $n$ over the ring $F_{2}+uF_{2}$. We find a set of generators for each $(1+u)$-constacyclic code and its dual. We study the rank of cyclic codes and find their minimal spanning sets. We prove that the Gray image of a $(1+u)$-constacyclic code is a binary cyclic code of length $2n$. We conclude by giving examples of constacyclic codes and their Gray image binary codes. We give a direct construction of a $[12,7,4]$ linear binary cyclic code that match the Hamming distance of the best binary code with length 12 and dimension 7.}, identifier = {05591600}, }