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:: Volume 7, Issue 1 (Vol.7, No. 1, Spring 2021) ::
mr 2021, 7(1): 83-90 Back to browse issues page
Gray Images of Constacyclic Codes Over Some Polynomial Residue Rings
Reza Sobhani
University of Isfahan , r.sobhani@sci.ui.ac.ir
Abstract:   (418 Views)
Let  be the quotient ring    where  is the finite field of size   and  is a positive integer. A Gray map  of length  over  is a special map from  to ( . The Gray map   is said to be a ( )-Gray map if the image of any -constacyclic code over    is a -constacyclic code over the field   . In this paper we investigate the existence of   ( )-Gray maps over . In this direction, we find an equivalent condition for such maps. Then we prove that if  is a        ( )-Gray map of length  over  and also  then we must have       ,   and  divides the length of  that is . We also prove that if   then we must have      . Moreover, we determine all of such maps over . Finally, we introduce a             ( , )-Gray map of length    over  where ../files/site1/files/71/8.pdf
Keywords: Gray map, constacyclic code, chain ring, polynomial residue ring.
Full-Text [PDF 478 kb]   (71 Downloads)    
Type of Study: Original Manuscript | Subject: alg
Received: 2018/03/4 | Accepted: 2019/09/1 | Published: 2021/05/31 | ePublished: 2021/05/31
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Sobhani R. Gray Images of Constacyclic Codes Over Some Polynomial Residue Rings. mr. 2021; 7 (1) :83-90
URL: http://mmr.khu.ac.ir/article-1-2753-en.html


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Volume 7, Issue 1 (Vol.7, No. 1, Spring 2021) Back to browse issues page
پژوهش‌های ریاضی Mathematical Researches
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