Gray Images of Constacyclic Codes Over Some Polynomial Residue Rings

Author
Reza Sobhani
University of Isfahan
10.52547/mmr.7.1.83
Abstract
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
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