TY - JOUR
T1 - Gray Images of Constacyclic Codes Over Some Polynomial Residue Rings
TT - تصویر گری کدهای ثابتدوری روی برخی از حلقههای چندجملهای خارجقسمتی
JF - khu-mmr
JO - khu-mmr
VL - 7
IS - 1
UR - http://mmr.khu.ac.ir/article-1-2753-en.html
Y1 - 2021
SP - 83
EP - 90
KW - Gray map
KW - constacyclic code
KW - chain ring
KW - polynomial residue ring.
N2 - 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
M3
ER -