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Paper IPM / M / 14858  


Abstract:  
n this study, we consider the finite (not necessary commutative) chain ring R:=\mathbb F_{pm}[u,θ]/ < u^{2} > , where Î¸ is an automorphism of \mathbb F_{pm}, and completely explore the structure of left and right cyclic codes of any length N over R, that is, left and right ideals of the ring S:=R[x]/ < x^{N}−1 > . For a left (right) cyclic code, we determine the structure of its right (left) dual. Using the fact that selfdual codes are bimodules, we discuss on selfdual cyclic codes over R. Finally, we study Gray images of cyclic codes over R and as some examples, three linear codes over \mathbb F_{4} with the parameters of the best known ones, but with different weight distributions, are obtained as the Gray images of cyclic codes over R.
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