Ontology type: schema:ScholarlyArticle Open Access: True
2016-08-11
AUTHORSHaifeng Yu, Yu Wang, Minjia Shi
ABSTRACTConstacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z 4 + uZ 4 of any length are studied. A new Gray map between Z 4 + uZ 4 and Z 4 (4) is defined. By means of this map, it is shown that the Z 4 Gray image of a (1 + u)-constacyclic code of length n over Z 4 + uZ 4 is a cyclic code over Z 4 of length 4n. Furthermore, by combining the classical Gray map between Z 4 and F 2 (2), it is shown that the binary image of a (1 + u)-constacyclic code of length n over Z 4 + uZ 4 is a distance invariant binary quasi-cyclic code of index 4 and length 8n. Examples of good binary codes are constructed to illustrate the application of this class of codes. More... »
PAGES1325
http://scigraph.springernature.com/pub.10.1186/s40064-016-2717-0
DOIhttp://dx.doi.org/10.1186/s40064-016-2717-0
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PUBMEDhttps://www.ncbi.nlm.nih.gov/pubmed/27563520
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