Abstract:
We study the structure of (1 + u)-constacyclic codes of an arbitrary length n over the ring F-2 + uF(2). We. nd a set of generators for each (1 + u)-constacyclic code and its dual. We study the rank of cyclic codes and. nd 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. (C) 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
