Constacyclic codes over F

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• 作者：Taher Abualrub ; Irfan Siap
• 关键词： ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V04-4VPV5JR-1&_mathId=mml8&_user=10&_cdi=5636&_pii=S0016003209000155&_rdoc=7&_issn=00160032&_acct=C000050221&_version=1&_userid=10&md5=de26e
• 刊名：Journal of The Franklin Institute
• 出版年：2009
• 出版时间：June 2009
• 年：2009
• 卷：346
• 期：5
• 页码：520-529
• 全文大小：160 K

文摘

We study the structure of (1+u)-constacyclic codes of an arbitrary length n over the ring F₂+uF₂. 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.